Algebra 2 CHAMP Block Set

+3x² + 2x + 8

(-4x² - x + 9) + (x² + 3x - 1)

-3x² - 2x

(-x² + 3x) - (5x + 2x²)

-2y³ + yx² + 7

(-y³ + 8yx² + 5) - (7yx² - 2 + y³)

10x²-67x-21

(10x+3)(x-7)

-2x² + 13x - 3

(5x² + 6x + 2) - (7x² - 7x + 5)

7x² - 4x - 2

(5x² - 3x + 2) + (-x + 2x² - 4)

81x²-16

(9x+4)(9x-4)

x²+8x+12

(X+6)(x+2)

Solve This Equation by Factoring. p^2+16p+64

(b + 8)^2

Solve the Equation by Grouping: c^2+2c-15.

(c+5)(c-3)

Solve the Equation by Factoring: q^2+2q−24.

(q+6)(q-4)

x² + 2x + 1

(x + 1)²

x² - 8x - 20

(x + 2)(x - 10)

x² - 5x - 24

(x + 3)(x - 8)

x² - 2x - 35

(x + 5)( x - 7)

x² - 25

(x + 5)(x - 5)

x² + x - 30

(x + 6)(x - 5)

6x² - 7x -6

(x² - 4x - 1) + (-5 + 5x² - 3x)

x³ - 6x² - 6x

(x³ + 2x²) - (6x - 4x² + 2x³)

6n(2n + 3)

12n^2 + 18n

Example for p: 5x³+4x²-2x+9

P: 9 ---> 1, 3, 9

zeroes of a function

The answer(s) to the function. Input value that produces an output of zero.

Quadratic Formula

The only way of solving quadratic equations that can be used in any problem. Written out, it is x = -b ± √(b² - 4ac)/2a.

q

first number of x in the equation (the leading coefficient)

(x+1)²

x²+2x+1

(x-4)(x+6)

x²+2x-24

(x+7)(x-5)

x²+2x-35

(x-7)(x+9)

x²+2x-63

(x+4)(x-2)

x²+2x-8

(x+30)(x+1)

x²+31x+30

(x+2)(x+30)

x²+32x+60

(x-2)(x+40)

x²+38x-80

(x+5)(x-2)

x²+3x-10

(x-4)(x+7)

x²+3x-28

(x+8)(x-5)

x²+3x-40

(x+11)(x-8)

x²+3x-88

(x+2)(x+40)

x²+42x+80

(x+9)(x-9)

x²-81

(x-6)(x-2)

x²-8x+12

(x-4)²

x²-8x+16

(x-7)(x-1)

x²-8x+7

(x+3)(x-3)

x²-9

(x-8)(x-1)

x²-9x+8

(x+3)(x-4)

x²-x-12

(x-6)(x+5)

x²-x-30

(x+6)(x-7)

x²-x-42

(x-3)(x+2)

x²-x-6

Solve the Equation by Factoring: y^2-4y+24.

y = (2±2i√5)

144x²-25

(12x-5)(12x+5)

7x - 5y + 4z

(2x + 6y - 3z) + (4x + 6z - 8y) + (x - 3y + z)

2x² - 7x + 3

(2x - 1)(x - 3)

2x² + 2x - 12

(2x - 4)(x + 3)

8x²-6x-5

(2x+1)(4x-5)

4x²+4x-3

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

6x²+x-12

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

8x²+18x+9

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

8x²+6x-35

(2x+5)(4x-7)

6x²+25xy+11y²

(2x+y)(3x+11y)

4x²-8x+3

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

2x²+3x−2

(2x-1)(x+2)

2x²−35x+17

(2x-1)(x-17)

6x²-x-12

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

6x²-17x+12

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

6x²-17x+5

(2x-5)(3x-1)

3x² + x + 7

(2x² + 6x) + (x² - 5x + 7)

2x² + x - 6

(2x² - 3x + 1) + (4x - 7)

3x²+19x+20

(3x+4)(x+5)

6x²+7x-5

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

3x²+4x-15

(3x-5)(x+3)

-5x² + 3x - 2

(3x² + 7x - 1) - (4x + 8x² + 1)

-3x + 4

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

24x²+18x+3

(4x+1)(6x+3)

4x²-11x-3

(4x+1)(x-3)

8x²+6x-5

(4x+5)(2x-1)

8x²+18x-5

(4x-1)(2x+5)

4x²+x-3

(4x-3)(x+1)

9x² + x

(4x² + 2x + 2) + (5x² - 2 - x)

-3x² + 3x -12

(4x² + 2x - 8) - (7x² + 4 - x)

4x² - 6x - 1

(4x² + 8x + 2) - (2x + 3)

7x² - 3x + 1

(4x² - 2x - 3) + (3x² - x + 4)

5x² - 2x + 8

(4x² - 3x + 10) + (x² + x - 2)

10x²+11x−8

(5x+8)(2x-1)

5x²+38x-16

(5x-2)(x+8)

10x²-x-3

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

5x²+16x-16

(5x-4)(x+4)

-4x + 6 - 13

(5x² - 8 + 2x) - (x + 9x² + 5)

30x²+43x+15

(6x+5)((5x+3)

6x²+11x+5

(6x+5)(x+1)

6x²+29x-5

(6x-1)(x+5)

x² - 10x + 1

(6x² - 7x - 3) - (5x² - 1 + 2x) - (2x² - 3 + x)

4x² - 9x + 5

(6x² - x + 1) - (-4 + 2x² + 8x)

Solve the Equation by Grouping: 7k^2−43k + 6.

(7k−1)(k−6)

49x²-84x+36

(7x-6)(7x-6)

8x² - 3x - 5

(7x² + 2 - x) + (x² - 7 - 2x)

8x²-39x-5

(8x+1)(x-5)

8x²-21x-9

(8x+3)(x-3)

24x²-48x+9

(8x-3)(3x-3)

8x²+3x-5

(8x-5)(x+1)

9x² - x - 3

(8x² + x - 6) - (-x² + 2x -3)

x² - 10x + 25

(x - 5)²

x²-4x-5

(x+1)(x-5)

2x²+15x-50

(x+10)(2x-5)

x²+6x−40

(x+10)(x-4)

x²+21x+38

(x+2)(x+19)

x²−13x−30

(x+2)(x-15)

One factor of g(x)= x³-x²-9x-9 is x-3. Find the remaining factors.

(x+3)(x+1)

x²+7x+12

(x+3)(x+4)

x²−15x−54

(x+3)(x-18)

x²-x-12

(x+3)(x-4)

x²+7x+10

(x+5)(x+2)

x²+11x+30

(x+5)(x+6)

x²+9x-10

(x-1)(x+10)

x²+2x-8

(x-2)(x+4)

x²−18x+45

(x-3)(x-15)

x²-5x-14

(x-7)(x+2)

x²-4x-21

(x-7)(x+3)

-4x² + 2y² - 1

(x² + y² - 6) - (5x² - y² - 5)

x³ - 3x² + 8x + 9

(x³ - 2x² + 4x + 6) - (-4x + x² - 3)

9x - 6

(x³ - 3x + 1) - (x³ + 7 - 12x)

Solve the Equation by Grouping: x^2-7x+12.

(x−3)(x−4)

Solve This Equation by Grouping. y^2-7y+12

(y-3)(y-4)

-x²+x+6

-(x+2)(x-3)

-2x²+4x+70

-2(x-7)(x+5)

-4(n+1)

-4n-4

Example of negative real zeros

-5, -4, -8

(-5n+6)(n+5)

-5n^2-19n+30

-9x²+9x+108

-9(x+3)(x-4)

-x³+5x²-6x

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

Example of positive real zeros

1, 2, 3

(2n+2)(6n+1)

12n^2+14n+2

(2r-3)(9r-6)

18r^2-39r+18

6x²-10xy+4y²

2(3x-2y)(x-y)

Solve This Equation by Factoring. f^2 + 6n -108.

2(f-6)(f+9)

(3n+5)(7n+8)

21n^2+59n+40

(n+4)(2n+8)

2n^2+16n+32

2x² - 4x

2x(x - 2)

(2x + 1)(x + 1)

2x² + 3x + 1

(2x + 3)(x + 1)

2x² + 5x + 3

Example of total of zeros: 5x³+4x²-2x+9

3 total number of zeros

3x²+3x−6

3(x+2)(x-1)

x(3x + 5)

3x² + 5x

(2n+4)(2n-4)

4n^2 - 16

(n-5)(4n-8)

4n^2-28n+40

8x² - 4x

4x(2x - )

8x⁴+4x³-12x²

4x² (x-1)(2x+3)

5x²+15x+10

5(x+2)(x+1)

(n+2)(5n+9)

5n^2+19n+18

(5n+9)(n+4)

5nc^2+29n+36

21x²−70x+49

7(3x-7)(x-1)

(7n-9)(n-5)

7n^2-44n+45

(4n+1)(2n+1)

8n^2+26n+6

(9n-4)(n-6)

9n^2-58n+24

Example for factor with given f(x)=0: x³-2x²-19x+20 f(5)=0

Answer: (x+4)(x-1)(x-5)

(2 - 3m)(4 + 6m + 9m²)

Factor Completely

(2a - 5)(2a + 5)

Factor Completely

(2n² + 5)(5n - 7)

Factor Completely

(3a + 7)(2a + 3)

Factor Completely

(3v + 2)(v - 1)

Factor Completely

(3x - 1)(x + 3)

Factor Completely

(3x² - 2)(x - 1)(x + 1)

Factor Completely

(4k + 1)(4k - 1)

Factor Completely

(4m + 1)²

Factor Completely

(4n - 1)²

Factor Completely

(4x + 3)(16x² - 12x + 9)

Factor Completely

(5 + 3a)(25 - 15a + 9a²)

Factor Completely

(5a² + 2)(7a - 1)

Factor Completely

(5x - 6)(25x² + 30x + 36)

Factor Completely

(7x² + 2)(x² + 2)

Factor Completely

(m² + 1)(m² - 8)

Factor Completely

(n - 7)(10n + 1)

Factor Completely

(r + 6)(r - 9)

Factor Completely

(x - 9)(x - 4)

Factor Completely

(x² - 5)(x² + 3)

Factor Completely

2(1 - r)²

Factor Completely

2(2n + 3)(5n + 2)

Factor Completely

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

Factor Completely

2(3a + 1)(9a² - 3a + 1)

Factor Completely

2(p - 9)(p + 8)

Factor Completely

3(2x + 5)²

Factor Completely

3(5u + 1)(25u² - 5u + 1)

Factor Completely

3(7n + 8)(n + 5)

Factor Completely

3x(1 - 6m)(1 + 6m + 36m²)

Factor Completely

4(4k² - 3)(5k + 1)

Factor Completely

5(5p + 4)(5p - 4)

Factor Completely

5n(n - 8)(n - 4)

Factor Completely

6(2r + 5)(r - 4)

Factor Completely

6(x - 1)(9x - 8)

Factor Completely

7(6x² - 7)(6x - 1)

Factor Completely

a(u - 4)(u² + 4u + 16)

Factor Completely

possible rational zeros

Use p & q, p over q will be the possible zeros

Factoring

Using the FOIL method, you distribute and then add like terms. To solve, you find a number that is added to your 'b' value and multiplied to your 'c' value.

Completing the Square

a process used to make a quadratic expression into a perfect square trinomial. You start by moving 'c' to the right, dividing by 'a', completing the square, then factoring.

Solve by Grouping

a way to solve quadratic equations in which you separate the equation into different groups and solve them individually.

negative real zeros

all the negative zeros except imaginary numbers

all zeros

all the numbers including imaginary numbers

positive real zeros

all the positive zeros except imaginary numbers

real zeros

any number except imaginary numbers

Synthetic Substitution

basically synthetic division using the x in the f(x)

p

last number of the equation without an x (the constant term)

(n - 1)(n+1)

n^2 - 1

(n+7)(n+8)

n^2+15n+56

(n+6)(n-4)

n^2+2n-24

(n-7)(n+8)

n^2+n-56

(n-7)(n-3)

n^2-10n+21

(n-7)(n-8)

n^2-15n+56

(n-8)^2

n^2-16n+64

(n+4)(n-9)

n^2-5n-36

(n+7)(n-8)

n^2-n-56

(n^2-8)(n+4)

n^3+4n^2-8n-32

(n+2)(n^2+3n+6)

n^3+5n^2+12n+12

Example for q: 5x³+4x²-2x+9

q: 5 ---> 1, 5

total number of zeros

the degree of the equation

Factor with given f(x)=0

use x in f(x) in synthetic substitution to find the binomial equation, then factor and add the equation for f(x)

x² + 4x

x(x+4)

Solve this Equation Using the Quadratic Formula: x^2+4x+2=0.

x= -4±2√2/2

Solve the Equation by Using the Quadratic Formula: w^2+39=-18w.

x=(-18±2√3)/4

Solve This Equation Using the Quadratic Formula. x^2+5x+3=0

x=-5±√13/2

Solve the Equation by Using the Quadratic Formula: x^2=x+3.

x=1±√13/2

x = -2

x² + 4x + 4 = 0

(x + 4)(x + 1)

x² + 5x + 4

x = -1 or x = -4

x² + 5x + 4 = 0

x = -2 or x = -3

x² + 5x + 6 = 0

(x - 4)(x + 10)

x² + 6x - 40

(x + 6)(x + 1)

x² + 7x + 6

(x - 3)(x + 4)

x² + x - 12

x = 3 or x = -4

x² + x − 12 = 0

(x - 4)(x + 2)

x² - 2x - 8

(x - 2)²

x² - 4x + 4

x(x - 5)

x² - 5x

(x - 3)(x + 3)

x² - 9

x = 1 or x = -1

x² − 1

x = -1 or x = 4

x² − 3x − 4 = 0

x = 4 or x = -1

x² − 3x − 4 = 0

x = 3 or x = 2

x² − 5x + 6 = 0

x = 3

x² − 6x + 9 = 0

x = -2 or x = 3

x² − x − 6 = 0

(x+7)(x+3)

x²+10x+21

(x+4)(x+6)

x²+10x+24

(x+5)²

x²+10x+25

(x+12)(x-2)

x²+10x-24

(x+1)(x+10)

x²+11x+10

(x+9)(x+2)

x²+11x+18

(x+8)(x+3)

x²+11x+24

(x+4)(x+7)

x²+11x+28

(x+5)(x+6)

x²+11x+30

(x+15)(x-4)

x²+11x-60

(x+1)(+11)

x²+12x+11

(x+3)(x+9)

x²+12x+27

(x+7)(x+5)

x²+12x+35

(x+6)²

x²+12x+36

(x+10)(x+3)

x²+13x+30

(x-2)(x+15)

x²+13x+30

(x+8)(x+5)

x²+13x+40

(x+6)(x+7)

x²+13x+42

(x+12)(x+2)

x²+14x+24

(x+7)²

x²+14x+49

(x+4)(x+11)

x²+15x+44

(x+6)(x+10)

x²+16x+60

(x+7)(x+9)

x²+16x+63

(x+8)²

x²+16x+64

(x-4)(x+20)

x²+16x-80

(x+15)(x+2)

x²+17x+30

(x+12)(x+5)

x²+17x+60

(x-3)(x+20)

x²+17x-60

(x+9)²

x²+18x+81

(x+15)(x+4)

x²+19x+60

(x+11)(x+8)

x²+19x+88

(x+3)(x+20)

x²+23x+60

(x+4)(x+20)

x²+24x+80

(x-2)(x+30)

x²+28x-60

(x+30)(x-1)

x²+29x-30

(x+2)²

x²+4x+4

(x+6)(x-2)

x²+4x-12

(x+7)(x-3)

x²+4x-21

(x-6)(x+10)

x²+4x-60

(x+2)(x+3)

x²+5x+6

(x+8)(x-3)

x²+5x-24

(x+6)(x-1)

x²+5x-6

(x+4)(x+2)

x²+6x+8

(x+3)²

x²+6x+9

(x-3)(x+9)

x²+6x-27

(x+2)(x+5)

x²+7x+10

(x+3)(x+4)

x²+7x+12

(x+6)(x+1)

x²+7x+6

(x+9)(x-2)

x²+7x-18

(x+10)(x-3)

x²+7x-30

(x-4)(x+11)

x²+7x-44

(x+12)(x-5)

x²+7x-60

(x+8)(x-1)

x²+7x-8

(x+6)(x+2)

x²+8x+12

(x+4)²

x²+8x+16

(x+7)(x+1)

x²+8x+7

(x+8)(x+1)

x²+9x+8

(x+6)(x-5)

x²+x-30

(x-6)(x+7)

x²+x-42

(x+3)(x-2)

x²+x-6

(x+1)(x-1)

x²-1

(x+10)(x-10)

x²-100

(x-7)(x-3)

x²-10x+21

(x-4)(x-6)

x²-10x+24

(x-5)²

x²-10x+25

(x-12)(x+2)

x²-10x-24

(x-1)(x-10)

x²-11x+10

(x-9)(x-2)

x²-11x+18

(x-8)(x-3)

x²-11x+24

(x-4)(x-7)

x²-11x+28

(x-5)(x-6)

x²-11x+30

(x-15)(x+4)

x²-11x-60

(x-1)(x-11)

x²-12x+11

(x-3)(x-9)

x²-12x+27

(x-7)(x-5)

x²-12x+35

(x-6)²

x²-12x+36

(x-10)(x-3)

x²-13x+30

(x-15)(x+2)

x²-13x+30

(x-8)(x-5)

x²-13x+40

(x-6)(X-7)

x²-13x+42

(x-12)(x-2)

x²-14x+24

(x-7)²

x²-14x+49

(x-4)(x-11)

x²-15x+44

(x+4)(x-4)

x²-16

(x-6)(x-10)

x²-16x+60

(x-7)(x-9)

x²-16x+63

(x-8)²

x²-16x+64

(x+4)(x-20)

x²-16x-80

(x-15)(x-2)

x²-17x+30

(x-12)(x-5)

x²-17x+60

(x+3)(x-20)

x²-17x-60

(x-9)²

x²-18x+81

(x-15)(x-4)

x²-19x+60

(x-11)(x-8)

x²-19x+88

(x-3)(x-20)

x²-23x+60

(x-4)(x-20)

x²-24x+80

(x+5)(x-5)

x²-25

(x+2)(x-30)

x²-28x-60

(x-30)(x+1)

x²-29x-30

(x-1)²

x²-2x+1

(x+4)(x-6)

x²-2x-24

(x-7)(x+5)

x²-2x-35

(x+7)(x-9)

x²-2x-63

(x-4)(x+2)

x²-2x-8

(x-30)(x-1)

x²-31x+30

(x-2)(x-30)

x²-32x+60

(x+6)(x-6)

x²-36

(x+2)(x-40)

x²-38x+80

(x-5)(x+2)

x²-3x-10

(x+4)(x-7)

x²-3x-28

(x-8)(x+5)

x²-3x-40

(x-11)(x+8)

x²-3x-88

(x+2)(x-2)

x²-4

(x-2)(x-40)

x²-42x+80

(x+7)(x-7)

x²-49

(x-2)²

x²-4x+4

(x-6)(x+2)

x²-4x-12

(x-7)(x+3)

x²-4x-21

(x+6)(x-10)

x²-4x-60

(x-6)(x+1)

x²-5x+6

(x-8)(x+3)

x²-5x-24

(x-6)(x+1)

x²-5x-6

(x+8)(x-8)

x²-64

(x-4)(x-2)

x²-6x+8

(x-3)²

x²-6x+9

(x+3)(x-9)

x²-6x-27

(x-2)(x-5)

x²-7x+10

(x-6)(x-1)

x²-7x+6

(x-9)(x+2)

x²-7x-18

(x-10)(x+3)

x²-7x-30

(x+4)(x-11)

x²-7x-44

(x-12)(x+5)

x²-7x-60

(x-8)(x+1)

x²-7x-8

Solve the Equation by Completing the Square: 4n^2+11n=15

{1,-3¾}

Solve the Equation by Completing the Square: x^2−2x=15

{5,-3}