Question

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. gfc 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 $64x^2$?
$32x^5$
$32x^2$
$32x^3$
$32x$

Explanation:

Step1: Find GCF of coefficients

Factor 96 and 64:
\( 96 = 2^5 \times 3 \), \( 64 = 2^6 \).
GCF of 96 and 64 is \( 2^5 = 32 \).

Step2: Find GCF of variables

For \( x^5 \) and \( x^2 \), GCF is \( x^{\min(5,2)} = x^2 \).

Step3: Multiply GCFs

Multiply coefficient GCF (32) and variable GCF (\( x^2 \)): \( 32x^2 \).

Answer:

32\( x^2 \) (corresponding to the option "32\( x^2 \)")