Sturgeon's: Solving Quadratic Equations by Factoring

Solve by Factoring with a GCF other than 1

100

Write in factored form then solve.

9x² - 81x = 0

FF  9x(x - 9) = 0

Solutions: x = 0, 9

200

Write in factored form, then solve.

 10x² - 2x = 0

FF:  2x(5x - 1) = 0

Solutions: x = 0, 1/5

300

Write in factored form, then solve.

 18x² - 24x = 0

FF:   6x(3x - 4) = 0

Solutions: x = 0, 4/3

400

Write in factored form, then solve.

 20x² - 15x = 0

FF:  5x(4x - 3) = 0

Solutions: x = 0, 3/4

500

Factor completely and solve.

48x^2 = 20x

FF: 4x(12x - 5) = 0

Solutions: x = 0, 5/12

Difference of Two Squares

100

Write in factored form then solve.

x² - 1 = 0

FF:  (x+1)(x-1) = 0

Solutions:  x = -1, 1

200

Write in factored form, then solve.

 x² - 4 = 0

FF:  (x + 2)(x - 2) = 0

Solutions: x = -2, 2

300

Write in factored form, then solve.

4x² - 49 =0

(2x+7)(2x-7) = 0

x=-7/2, 7/2

400

Write in factored form, then solve.

169x² - 4 =0

FF: (13x + 2)(13x - 2) = 0

Solutions: x = -2/13, 2/13

500

Factor completely, then solve.

64x^2-4=0

FF:  4(4x+1)(4x-1) = 0

Solutions: x = -1/4, 1/4

Find the ZEROS by factoring

100

Find the zeros by factoring. Show factored form and solutions.

f(x) = x² - 6x + 8 

FF:  0 = (x - 2)(x - 4)

x = 2, 4

200

Find the zeros. First write in factored form.

f(x) =  x² - 2x - 24

FF: (x-6)(x+4) = 0

{-4, 6}

300

Find the zeros. Write in factored form.

f(x) = 4x^2 -23x-6

FF:   0 = (4x + 1)(x - 6)

x = -1/4, 6

400

Find the zeros by factoring. Show factored form.

g(x) = 15x² - x - 2

(3x+1)(5x-2) =0

x = -1/3, 2/5

500

Find the zeros by factoring. Show factored form.

f(x) = 100x^2 -9

FF:  0 = (10x + 3)(10x - 3)

x = -3/10, 3/10

Writing Equations in Factored Form

100

Write the equation in factored form.

 x² + 6x + 5 = 0

(x+1)(x+5) = 0

200

Write the equation in factored form.

 x² - 81 = 0

(x+9)(x-9) = 0

300

Write the equation in factored form.

 6x² + 12x = 0

6x(x+2) = 0

400

Write the equation in factored form.

2x² + 9x + 4 = 0

(2x+1)(x+4) = 0

500

Solve by factoring.

20x²+48x = 5

x = 1/10, -5/2

Random Questions

100

What is the GCF of the expression?

14x^2 -21x 

7x

200

What is the GCF of the expression?

6x^2 -24x +16 

GCF:  2

300

Write in factored form and solve.

 3n² - 25n + 28=0

FF:  (3n - 4)(n - 7)=0

Solutions: n = 4/3, 7

400

Solve the following quadratic equation by factoring: 

5n² + 41n - 12 = -4 + 2n

n=-8, 1/5

500

Factor completely and solve. 

9x² + 10x - 30= 7x

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

Solutions: x = -2, 5/3