Algebra 1 Chapter 7 - Factoring

Factoring a GCF

100

6ab - 3a

3a(2b - 1) 

200

7a³ - 14a + 7

7(a³ - 2a + 1)

300

8s⁸ t⁴ + 20s⁴ t³

4s⁴t³(2s⁴t + 5)

400

10x² + 25x - 100 

5(2x² + 5x - 20) 

500

8x⁴ + 8x³ - 8x²

8x²(x² + x - 1)

Factoring Trinomials a=1

100

x² + 16 x + 63

(x + 9)(x + 7)

200

q² – 12q + 20

(q- 2)(q-10)

300

x² + 5x – 14

(x + 7)(x - 2)

400

k² + 4k – 96

What is (k + 12)(k - 8)

500

a² – 7a – 18

(a - 9)(a + 2)

Factoring Trinomials a>1

100

2w² + 13w + 15

(2w + 3)(w + 5)

200

3d² + 20d + 12

(3d + 2)(d + 6)

300

3x² + 9x - 84

3(x + 7)(x - 4)

400

24c² + 96c + 9

3(8c² + 32c + 3) can't go further!

500

6r² - 10r - 24

What is 2(3r + 4)(r - 3)

Factoring 4 Term Polynomials

100

3x² + 6x + 4x + 8

(x + 2)(3x + 4)

200

x³ - 4x² + 3x - 12

(x² + 3)(x - 4)

300

5t⁴ + 20t³ + 6t + 24 

(5t³ + 6)(t + 4)

400

3x³ + 2x² - 12x - 8

(x² - 4)(3x+ 2)

500

2x² + 4x + 16x + 32 

2(x + 8)(x + 2) 

Challenging Problems!

100

What trinomial would be factored to: (y – 4)(y + 7)

y² + 3y - 28

200

What trinomial would be factored to: (3x + 1)(5x – 3)

15x² - 4x - 3

300

What trinomial would be factored to: (5s + 2)²

25s² +20s + 4

400

A brown rectangular tarp has the side length of (x + 8) and the width of (2x - 3). What is the area of the brown part of the tarp?

2x² + 13x - 24

500

A football field has the area of 3x² + 11x - 20, what are the length and width of the field? 

(3x - 4)(x + 5)