Question

determining the gcf of two monomials

find the gcf of (96x^5) and (64x^2).

1. gcf of 96 and 64:

(64 = (2)(2)(2)(2)(2)(2))
(96 = (2)(2)(2)(2)(2)(3))
(gcf = (2)(2)(2)(2)(2) = 32)

1. gcf of (x^5) and (x^2):

(x^5 = (x)(x)(x)(x)(x))
(x^2 = (x)(x))
(gcf = (x)(x) = x^2)

what is the gcf of (96x^5) and (64x^2)?

( ) (32x)
( ) (32x^2)
( ) (32x^3)
( ) (32x^5)

Explanation:

Find the GCF of the numerical coefficients

$$
LATEXBLOCK0
$$

Find the GCF of the variable parts

$$
LATEXBLOCK1
$$

Combine the numerical and variable GCFs

$$ \text{GCF}(96x^5, 64x^2) = 32 \cdot x^2 = 32x^2 $$

Answer:

• (A) \(32x\)
• (B) \(32x^2\) (Correct answer)
• (C) \(32x^3\)
• (D) \(32x^5\)