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
