Question

omial by factoring out the greatest common factor. if it cannot be fa
$4y^5 - 12y^2 - 16y^7$
er (opens in new window) 2 points
i replace the entered answer value(s) with the radio button value. if t
er is used.

Explanation:

Step1: Find the GCF of coefficients

The coefficients are 4, -12, -16. The GCF of 4, 12, 16 is 4.

Step2: Find the GCF of variables

For the variable \( y \), the lowest power among \( y^5 \), \( y^2 \), \( y^7 \) is \( y^2 \).

Step3: Factor out the GCF

Factor out \( 4y^2 \) from \( 4y^5 - 12y^2 - 16y^7 \):
\( 4y^2(y^3 - 3 - 4y^5) \) (we can also re - order the terms inside the parentheses as \( 4y^2(- 4y^5 + y^3 - 3) \) or \( - 4y^2(4y^5 - y^3 + 3) \), but factoring out the positive GCF first gives \( 4y^2(y^3 - 3 - 4y^5) \))

Answer:

\( 4y^2(-4y^5 + y^3 - 3) \) (or equivalent forms like \( 4y^2(y^3 - 3 - 4y^5) \))