What is the GCF of a polynomial?

The largest expression that divides evenly into every term — can include numbers and variables.

How do I find the GCF with variables?

Find the GCF of coefficients, then take the lowest power of each variable in all terms. GCF of 6x³ and 9x² is 3x².

It simplifies the remaining expression and often makes further factoring much easier.

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Name:Date:Class:

1.Factor:

72 x + 64

2.Factor:

12 x + 8

3.Factor:

5 x + 15

4.Factor:

49 x + 63

5.Factor:

7 x + 49

6.Factor:

48 x + 18

7.Factor:

5 x + 40

8.Factor:

42 x + 6

9.Factor:

6 x + 21

10.Factor:

35 x + 56

11.Factor:

8 x + 2

12.Factor:

8 x + 36

13.Factor:

40 x + 45

14.Factor:

32 x + 28

15.Factor:

81 x + 18

16.Factor:

14 x + 49

17.Factor:

54 x + 63

18.Factor:

36 x + 20

19.Factor:

28 x + 8

20.Factor:

8 x + 2

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Problem: Factor: 12x³ − 8x² + 4x

GCF of 12, 8, 4 is 4. Lowest x power is x¹. GCF = 4x.— 4x divides evenly into every term.
12x³/4x = 3x², 8x²/4x = 2x, 4x/4x = 1— Divide each term by 4x.
4x(3x² − 2x + 1)— Write the factored form.

Answer: 4x(3x² − 2x + 1)