Factoring Polynomials by GCF

GCF of Numbers

100

What is the greatest common factor of 10 and 5?

5

200

What is the greatest common factor of 4 and 30?

2

300

What is the greatest common factor of 12 and 5?

1

400

What is the greatest common factor of 50 and 120?

10

500

What is the greatest common factor of 120 and 24?

24

Binomials (GCF)

100

16p⁴ + 4p³

4p³(4p + 1)

200

9x + 36

9(x + 4)

300

6n³ - 3n⁵

3n³(2 - n²)

400

63x¹² − 35x⁶

7x⁶(9x⁶ - 5)

500

45b + 63 

9(5b + 7)

Trinomials (GCF)

100

14a + 21a² + 21a³

7a(2 + 3a + 3a²)

200

50p³ + 50p² - 20

10(5p³ + 5p² − 2)

300

9x⁶− 63x³ − 90x²

9x²(x⁴ - 7x - 10)

400

10n³ - 9n² + n

n(10n² - 9n + 1)

500

9x⁴y² - 15x³y + 3x²y

3x²y(3x²y - 5x + 1)

Negative Leading Coefficient

100

-6r⁵ - 6r⁴

-6r⁴(r + 1)

200

-20n³ - 35n² +20

-5(4n³  + 7n² - 4)

300

-90x⁵ + 100x + 60

-10(9x⁵ - 10x - 6)

400

-18n² + 15n - 15

-3(6n² - 5n +5)

500

-3k³ + 15k² - 6k

-3k(k² -5k + 2)

Difference of Squares

100

(m²-9)

(m+9)(m-9)

200

x²-16

(x+4)(x-4)

300

4x²-4

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

400

9x²-81

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

500

36x²-121

(6x+11)(6x-11)