Algebra IB FINAL Review

{-4/3, 1/6}

18x² + 10x = -11x + 4

x² + 11x + 28

(x + 4)(x + 7)

x² + 3x - 4

(x + 4)(x - 1)

4√3

Simplify √8 × √6

(-2x + 6)(3y - 2)

Factor -6xy + 4x + 18y - 12

(5x - 4)(2x + 5)

Factor 10x² + 17x - 20

2(3x - 2)(2x + 7)

Factor 12x² + 34x - 28

(3x - 4)(4x - 5y)

Factor 12x² - 15xy - 16x + 20y

2(3x + 2)(2x - 5)

Factor 12x² - 22x - 20

15xy(1 + 2xy)

Factor 15xy + 30x²y²

3(2x + 3)(2x - 2)

Factor 18x² + 15x - 18

2(x + 2)(x + 3)

Factor 2x² + 10x + 12

(x + 3)(2x + 3)

Factor 2x² + 3x + 6x + 9

5x²y(6x + 7y)

Factor 30x³y + 35x²y²

(x + 16)(x + 2)

Factor 32 + 18x + x²

8(4x + 3y²)

Factor 32x + 24y²

12xy(3y - 4x)

Factor 36xy² - 48x²y

(3x + 2)(x + 2)

Factor 3x² + 8x + 4

(x - 12)(x - 4)

Factor 48 - 16x + x²

4(x² + 4)

Factor 4x² + 16

(2x + 3)(2x - 1)

Factor 4x² + 4x - 3

(4x + 2)(x - 3)

Factor 4x² - 12x + 2x - 6

5x(x²y² + 2xy + 5)

Factor 5x³y² + 10x²y + 25x

8(8 - 5xy)

Factor 64 - 40xy

(2x + 5)(3y - 4)

Factor 6xy - 8x + 15y - 20

(3x - 1)(2x + 3)

Factor 6x² + 7x - 3

3xy(2x - y)

Factor 6x²y - 3xy²

15xy³(5x + 4)

Factor 75x²y³ + 60xy³

(4x - 3)(2x - 3)

Factor 8x² - 18x + 9

Prime

Factor 8x² - 5x - 10

8xy(xy - 3y² + 2)

Factor 8x²y² - 24xy³ + 16xy

3x(3ax² + 6bx + 8c)

Factor 9ax³ + 18bx² + 24cx

3xy²(3x² - 2y)

Factor 9x³y² - 6xy³

(x + 4)(x + 6)

Factor x² + 10x + 24

(x + 3)(x + 9)

Factor x² + 12x + 27

(x + 11)(x + 3)

Factor x² + 14x + 33

(x + 2)(x + 4)

Factor x² + 4x + 2x + 8

(x - 4)(x + 8)

Factor x² + 4x - 32

(x + 10)(x - 6)

Factor x² + 4x - 60

(x + 8)(x - 7)

Factor x² + x - 56

(x - 3)(x - 8)

Factor x² - 11x + 24

(x - 6)(x - 5)

Factor x² - 11x + 30

(x - 9)(x - 7)

Factor x² - 16x + 63

(x + 7)(x - 9)

Factor x² - 2x - 63

(x - 7)(x + 4)

Factor x² - 3x - 28

(x + 5)(x - 11)

Factor x² - 6x - 55

(x - 10y)(x + y)

Factor x² - 9xy - 10y²

(x - 8)(x + 7)

Factor x² - x - 56

(x - 8y)(x + 7y)

Factor x² - xy - 56y²

y = -2/3x + 2 and y = -2/3x - 2

What are the equations for this system?

y = -3 and y = x - 1

What are the equations for this system?

y = -3/2x + 3 and y = -3/2x + 1

What are the equations for this system?

y = -3/2x and y = -1/2x

What are the equations for this system?

y = 1/2x - 2 and x - 2y = 4

What are the equations for this system?

y = 2x + 1 and 2x - y = -1

What are the equations for this system?

y = 2x + 1 and y = -1/2x + 4

What are the equations for this system?

y = 3x - 4 and y = -x

What are the equations for this system?

infinitely many solutions

What is the SOLUTION to the system?

no solution

What is the SOLUTION to the system?

one solution; (-2, -3)

What is the SOLUTION to the system?

one solution; (0, 0)

What is the SOLUTION to the system?

one solution; (1, -1)

What is the SOLUTION to the system?

one solution; (2, 3)

What is the SOLUTION to the system?

-5

What is the leading coefficient for the polynomial (Hint: first put the polynomial in standard form): 6x - 2x² - 5x³ + 1

-2

What is the leading coefficient of: -2x⁷ - 5x + 8

5

What is the leading coefficient of: 5x⁵ + 8x² - 4

4x + 10

What is the perimeter of a rectangle with a length of x + 2 and a width of x + 3?

6x + 14

What is the perimeter of a rectangle with a length of x + 6 and a width of 2x + 1?

4x + 8

What is the perimeter of a square with a side length of x + 2?

4x - 24

What is the perimeter of a square with a side length of x - 6?

3x - 2y

What is the perimeter of a triangle with side lengths of 2x + 3y, 5x - 6y, and -4x + y?

no solution

solve by substitution: 2x + y = 5 and 2x + y = 7

infinitely many solutions

solve by substitution: 2x + y = 7 and y = -2x + 7

(6, -3)

solve by substitution: 2x - 3y = 21 and y = 3 - x

infinitely many solutions

solve by substitution: 3x + y = 8 and y = -3x + 8

no solution

solve by substitution: x = -5y + 4 and 3x + 15y = -1

(2, -3)

solve by substitution: x = 2 and 2x + y = 1

(-6, 1)

solve by substitution: x = y - 7 and x = -8y + 2

(-2, -4)

solve by substitution: y = 2x and x + 3y = -14

(1, 2)

solve by substitution: y = 2x and x + y = 3

no solution

solve by substitution: y = 3 and y = 5

no solution

solve by substitution: y = 3x + 5 and y = 3x + 4

(-1, 5)

solve by substitution: y = 3x + 8 and 5x + 2y = 5

infinitely many solutions

solve by substitution: y = 3x - 2 and y = 3x - 2

(3, 9)

solve by substitution: y = 3x and 2x + y = 15

(-2, -9)

solve by substitution: y = 4x - 1 and y = 2x - 5

(1, 4)

solve by substitution: y = 4x and x + y = 5

no solution

solve by substitution: y = 5x - 1 and y = 5x + 2

infinitely many solutions

solve by substitution: y = 5x - 9 and y = 5x - 9

(2, 1)

solve by substitution: y = x - 1 and x + y = 3

9x - 13y

(11x - 7y) - (2x + 6y)

6x² - 6

(2x + 2)(3x - 3)

4x³ + 12x² + 17x + 12

(2x + 3)(2x² + 3x + 4)

6x + 12y

(2x + 3y) + (4x + 9y)

2x² - 3x - 20

(2x + 5)(x - 4)

4x² + 4xy² + y⁴

(2x + y²)²

2x² - 18

(2x - 6)(x + 3)

4x⁴ + 12x²y² + 9y⁴

(2x² + 3y²)²

3x² + x + 7

(2x² + 6x) + (x² - 5x + 7)

8x⁴ + 8x³ + 10x² + 4x - 6

(2x² + x + 3)(4x² + 2x - 2)

4x⁴ - 12x³ + 8x² + 6x - 9

(2x² - 2x - 3)(2x² - 4x + 3)

-x² + 2x

(2x² - 5x) + (7x - 3x²)

3x² + 7x + 2

(3x + 1)(x + 2)

3x² - 5x - 2

(3x + 1)(x - 2)

9x² - 4

(3x + 2)(3x - 2)

6x³ + 21x² + 9x - 6

(3x + 3)(2x² + 5x - 2)

9x² + 3x - 6

(3x + 3)(3x - 2)

9x² - 49

(3x + 7)(3x - 7)

9x² - 9y²

(3x - 3y)(3x + 3y)

3x² + 2x - 21

(3x - 7)(x + 3)

9x⁴ - 6x³ - 17x² - 18x - 10

(3x² + 2x + 2)(3x² - 4x - 5)

6x⁴ + 7x³ + 27x² + 17x - 9

(3x² + 2x - 1)(2x² + x + 9)

9x⁴ - 6x²y + y²

(3x² - y)²

7x²y³ + 6xy

(3x²y³ + xy) + (4x²y³ + 5xy)

8x² + 6x + 1

(4x + 1)(2x + 1)

8x² + 18xy + 9y²

(4x + 3y)(2x + 3y)

16x² - 12x + 2

(4x - 2)(4x - 1)

-3x² + 3x - 12

(4x² + 2x - 8) - (7x² + 4 - x)

4x² + 6x - 1

(4x² + 8x + 2) - (2x + 3)

16x⁶ - 16x³y + 4y²

(4x³ - 2y)²

-3y + 4

(4y + 5) + (-7y - 1)

3x + 5y

(5x + 9y) - (2x + 4y)

3x + y + 1

(5x + y - 2) + (-2x + 3)

10x² - 19x + 6

(5x - 2)(2x - 3)

-2x² + 13x - 3

(5x² + 6x + 2) - (7x² - 7x + 5)

36 + 12x + x²

(6 + x)²

10x + 13y

(6x + 5y) + (4x + 8y)

42x² - 45x + 12

(6x - 3)(7x - 4)

10x² - 3x + 9

(6x² + 2x + 9) + (4x² - 5x)

4x² - 9x + 5

(6x² - x + 1) - (-4 + 2x² + 8x)

36x⁶ - 12x³y + y²

(6x³ - y)²

5x² + 24x - 5

(x + 5)(5x - 1)

x² + 6x + 5

(x + 5)(x + 1)

x² + 10x + 25

(x + 5)²

x² + 14x + 48

(x + 6)(x + 8)

x² - 2x - 48

(x + 6)(x - 8)

x² + 12x + 36

(x + 6)²

x² + 12x + 35

(x + 7)(x + 5)

x² + 2x - 35

(x + 7)(x - 5)

x² - 49

(x + 7)(x - 7)

x² + 14x + 49

(x + 7)²

x² - 64

(x + 8)(x - 8)

x² + 16x + 64

(x + 8)²

x² + 12x + 27

(x + 9)(x + 3)

x² + 6x - 27

(x + 9)(x - 3)

x² - 81

(x + 9)(x - 9)

x² + 18x + 81

(x + 9)²

x² + 2xy + y²

(x + y)²

5x² - 9x + 4

(x - 1)(5x - 4)

x² + x - 2

(x - 1)(x + 2)

x² + 4x - 5

(x - 1)(x + 5)

x² + 7x - 8

(x - 1)(x + 8)

x² - 3x + 2

(x - 1)(x - 2)

x² - 9x + 8

(x - 1)(x - 8)

x² - 2x + 1

(x - 1)²

x² - 20x + 100

(x - 10)²

x² - 22x + 121

(x - 11)²

x² - 24x + 144

(x - 12)²

x² + x - 6

(x - 2)(x + 3)

x² + 3x - 10

(x - 2)(x + 5)

x² - 4x + 4

(x - 2)(x - 2)

x² - 5x + 6

(x - 2)(x - 3)

x² - 7x + 10

(x - 2)(x - 5)

x² - 4x + 4

(x - 2)²

x² - 7x + 12

(x - 3)(x - 4)

x² - 6x + 9

(x - 3)²

x² + 3x - 28

(x - 4)(x + 7)

x² - 3x - 4

(x - 4)(x +1)

x² - 5x + 4

(x - 4)(x - 1)

x² - 11x + 28

(x - 4)(x - 7)

x² - 8x + 16

(x - 4)²

x² - 8xy + 16y²

(x - 4y)²

x² - 4x - 5

(x - 5)(x + 1)

x² - 25

(x - 5)(x + 5)

x² - 6x + 5

(x - 5)(x - 1)

x² - 10x + 25

(x - 5)²

x² + 2x - 48

(x - 6)(x + 8)

x² - 14x + 48

(x - 6)(x - 8)

x² - 12x + 36

(x - 6)²

x² - 2x - 35

(x - 7)(x + 5)

x² - 12x + 35

(x - 7)(x - 5)

x² - 14x + 49

(x - 7)²

x² - 16x + 64

(x - 8)²

x² - 6x - 27

(x - 9)(x + 3)

x² - 12x + 27

(x - 9)(x - 3)

x² - 18x + 81

(x - 9)²

2x² - 3xy + y²

(x - y)(2x - y)

-x² - 8x

(x² - 3x) - (2x² + 5x)

6x² - 7x - 6

(x² - 4x - 1) + (-5 + 5x² - 3x)

x² - 3x

(x² - x + 5) - (2x + 5)

2x² + x

(x² - x) + (2x + x²)

-4x³ - x²

x²(-4x + 5) - 6x²

(x - 5)(x + 9)

Factor x² + 4x - 45

(-1, 2)

2m + 3n = 4, -m + 2n = 5

(2.5, 0)

2x + 2y = 5, 4x - 4y = 10

(-3, 4)

2x + 3y = 6, x + 2y = 5

(-3, -5)

2x - 3y = 9, 5x + 3y = -30

-14x³ - 8x²

2x(-7x² - 4x)

2x² - 8x

2x(x - 4)

2x²y² + 2x²y³

2xy(xy + xy²)

(1, 1)

3a - b = 2, a + 2b = 3

(-3, 7)

3x + 4y = 19, 3x + 6y = 33

(2, -1)

3x + 4y = 2, 4x - 4y = 12

(-5, -4)

3x - 2y = -7, 2x - 5y = 10

infinitely many solutions

3x - 4y = -4, 6x - 8y = -8

(-1, -2)

3x - y = -1, -3x - y = 5

(10, 4)

3x - y = 26, -2x - y = -24

6x² + 6x - 3

3x(3x + 6) - 3(x² + 4x + 1)

(-1, 2)

4x + 5y = 6, 6x - 7y = -20

(-0.5, 2)

4x - 3y = -8, 2x + 2y = 3

(4, -2)

4x - 3y = 22, 2x - y = 10

(2, -1)

4x - y = 9, 5x + 2y = 8

-22x² + 2x + 8

4x(-5x - 3) - 2(x² - 7x - 4)

(-1, 1)

5x - y = -6, -x + y = 2

-4x³ + 3x² + 19x

5x(-7x + 3) + 2x(-2x² + 19x + 2)

15x²y² + 10xy²

5xy(3xy + 2y)

2x² - 63x + 15

6x(2x - 3) - 5(2x² + 9x - 3)

18x³y + 24xy²

6xy(3x² + 4y)

36√6

Simplify 4√3 × 3√18

-3√19 + 11√7

Simplify 5√19 + 4√28 - 8√19 + √63

6√2 + 6√5

Simplify 5√8 + 3√20 - √32

-5√13x

Simplify 7√13x - 14√13x + 2√13x

4√30

Simplify 8√30 - 4√30

3x² + 7x

Simplify x(3x + 2) + 5x

√11/11

Simplify √(1/7) × √(7/11)

3√2x / x²

Simplify √(18/x³)

√5 / 5

Simplify √(2/10)

√15 / 5

Simplify √(3/4) × √(4/5)

6√3

Simplify √108

6|x³|y²√3

Simplify √108x⁶y⁴

4√10

Simplify √160

2√5

Simplify √20

10√2

Simplify √200

2√6

Simplify √24

3√3

Simplify √27

3√2 + 13√3

Simplify √27 + √18 + √300

3|x|√3xy

Simplify √27x³y

10√3

Simplify √300

√6k / 4

Simplify √3k /√8

4√10

Simplify √40 - √10 + √90

3√5

Simplify √45

4√3

Simplify √48

-3√10

Simplify √5(5√2 - 4√8)

5√2

Simplify √50

5x²√2x

Simplify √50x⁵

2|x|y²√14y

Simplify √56x²y⁵

2√15 + 3√10

Simplify √6(√10 + √15)

2√15

Simplify √60

7√2

Simplify √7 × √14

2√3 / 3

Simplify √8 / √6

3√10

Simplify √90

|x|

Simplify √x²

x√x

Simplify √x³

x²√x

Simplify √x⁵

|x³|

Simplify √x⁶

x³√x

Simplify √x⁷

x⁴

Simplify √x⁸

x⁴√x

Simplify √x⁹

{-5/2, 4}

Solve (2y + 5)(y - 4)=0

{-2, 4/3}

Solve (4y + 8)(3y - 4)=0

{-6, 7/3}

Solve (a + 6)(3a - 7)=0

{-2, 3}

Solve (x - 3)(x + 2)=0

{2/5, 5/2}

Solve 10x² + 10 = 29x

{-3/2, 0}

Solve 14x² = -21x

{-1/3, 2/5}

Solve 15x² - x = 2

{-13, -4}

Solve 17x + x² = -52

{0, 5/6}

Solve 18x² = 15x

{-10, 0}

Solve 2x² + 20x=0

{-4, 0}

Solve 4x(x + 4)=0

{8, 10}

Solve 80 + x²= 18x

{0, 1/2}

Solve 8p² - 4p=0

{1/2, 3/4}

Solve 8x² - 10x + 3=0

{-13/4, 0}

Solve 8x² = -26x

{0, 3}

Solve 9x² = 27x

{-3½, 1}

Solve by using the Quadratic Formula. Round to the nearest tenth if necessary 2x²+5x-7=0

∅

Solve by using the Quadratic Formula. Round to the nearest tenth if necessary: 2x²+5x+4=0

{-4½, 1}

Solve by using the Quadratic Formula. Round to the nearest tenth if necessary: 2x²+7x=9

{½, 1}

Solve by using the Quadratic Formula. Round to the nearest tenth if necessary: 2x²-3x=-1

{-1.4, 0.7}

Solve by using the Quadratic Formula. Round to the nearest tenth if necessary: 3x²+2x-3=0

{-2/3, 3}

Solve by using the Quadratic Formula. Round to the nearest tenth if necessary: 3x²-7x-6=0

{-6, -5}

Solve by using the Quadratic Formula. Round to the nearest tenth if necessary: x²+11x+30=0

{-3.7, -0.3}

Solve by using the Quadratic Formula. Round to the nearest tenth if necessary: x²+4x=-1

{-5.4, -0.6}

Solve by using the Quadratic Formula. Round to the nearest tenth if necessary: x²+6x+3=0

{-4, 9}

Solve by using the Quadratic Formula. Round to the nearest tenth if necessary: x²-5x-36=0

{0.5, 6.5}

Solve by using the Quadratic Formula. Round to the nearest tenth if necessary: x²-7x=-3

no real solutions

Solve by using the Quadratic Formula. Round to the nearest tenth if necessary: x²-9x+22=0

{-4, 5}

Solve by using the Quadratic Formula. Round to the nearest tenth if necessary: x²-x-20=0

{0, 32}

Solve x(x - 32)=0

{-14, -3}

Solve x² + 17x + 42=0

{-9, 6}

Solve x² + 3x - 54=0

{-8, 4}

Solve x² + 4x = 32

{-12, 7}

Solve x² + 5x - 84=0

{-4, 16}

Solve x² - 12x - 64=0

{-4, 18}

Solve x² - 14x = 72

{5, 12}

Solve x² - 17x = -60

{-2, 28}

Solve x² - 26x = 56

{-7, 12}

Solve x² - 84 = 5x

{-2, 18}

Solve x² = 16x + 36

-3x² - 2x

(-x² + 3x) - (5x + 2x²)

x² + 3x + 2

(x + 1)(x + 2)

x² + 9x + 8

(x + 1)(x + 8)

x² - x - 2

(x + 1)(x - 2)

x² - 7x - 8

(x + 1)(x - 8)

x³ + 3x² + 6x + 4

(x + 1)(x² + 2x + 4)

x² + 2x + 1

(x + 1)²

x² - 100

(x + 10)(x - 10)

x² + 20x + 100

(x + 10)²

x² + 22x + 121

(x + 11)²

x² + 24x + 144

(x + 12)²

x² + 4x + 4

(x + 2)(x + 2)

x² + 5x + 6

(x + 2)(x + 3)

x² + 7x + 10

(x + 2)(x + 5)

x² - 4

(x + 2)(x - 2)

x² - x - 6

(x + 2)(x - 3)

x² - 3x - 10

(x + 2)(x - 5)

x² + 4x + 4

(x + 2)²

x² + 7x + 12

(x + 3)(x + 4)

x² - 9

(x + 3)(x - 3)

x² - x - 12

(x + 3)(x - 4)

x³ + 6x² + 14x + 15

(x + 3)(x² + 3x + 5)

x² + 6x + 9

(x + 3)²

x² + 6xy + 9y²

(x + 3y)²

x² + 5x + 4

(x + 4)(x + 1)

x² + x - 12

(x + 4)(x - 3)

x² - 16

(x + 4)(x - 4)

x² - 3x - 28

(x + 4)(x - 7)

x³ + 7x² + 6x - 24

(x + 4)(x² + 3x - 6)

x² + 8x + 16

(x + 4)²

x² + 8xy + 16y²

(x + 4y)²

9x² - 7x - 12

-2(3x³ + 5x + 6) + 3x(2x² + 3x + 1)

6n⁴ - 2n³ - 4n²

-2/3 n²(-9n² + 3n + 6)

-6x² + 15x

-2x(3x - 4) + 7x

6n⁴ - 9n³ - 12n²

-3n²(-2n² + 3n + 4)

-3x² + 3x + 3

-3x(7x - 2) + 3(x² + 2x + 1) - 3x(-5x + 3)

-3x³ - 6x²

-3x(x² + 2x)

-4x + 36x² + 8x³

-4x(1 - 9x - 2x²)

(6, 4)

-x + 3y = 6, x + 3y = 18

(5, 6)

-x + y = 1, x + y = 11

-11x² - 4x

-x(11x + 4)

-2x² + 3x

-x(2x - 8) - 5x

36 + 14√6

Simplify (2√2 + 2√3)(4√3 + 3√2)

2√30 + 30√2

Simplify (4√3 - 2√5)(3√10 + 5√6)

40 - 10√15

Simplify (5 - √15)²

4√3

Simplify (√10 + √6)(√30 - √18)

30√3 - 5√10

Simplify (√2 + 2√8)(3√6 - √5)

14√2

Simplify 2√32 + 3√50 - 3√18

14√5

Simplify 2√45 + 4√20

-10√5

Simplify 2√5 - 7√5 - 5√5

12√21 + 20√14

Simplify 2√7(3√12 + 5√8)

-√10 - 3√3

Simplify 3√10 + √75 - 2√40 - 4√12

90√2

Simplify 3√12 × 5√6

-x³ + x + 25

Write the polynomial in standard form: 25 - x³ + x

5x⁵ + 8x² - 15

Write the polynomial in standard form: 8x² - 15 + 5x⁵

(1, 0.2)

x + 10y = 3, 4x + 5y = 5

(-8, 0)

x + 4y = -8, x - 4y = -8

(11, 0)

x + 4y = 11, x - 6y = 11

(2, 1)

x - y = 1, x + y = 3

(0, -4)

x - y = 4, 2x + y = -4