Chapter 8.2, Problem 3STP

For Exercises $1-5,$ choose the correct letter.

How can the polynomial $6d^4+9d^3-12d^2$ be factored?

A. $3d^2\left(2d^2+3d-4\right)$

B. $3d^2\left(3d^2+6d-9\right)$

C. $3d\left(d^3+3d^2-4\right)$

D. $6d^2\left(d^2+3d^3-6\right)$

To determine

To choose: the correct factorized form of given expression.

Answer to Problem 3STP

A. $3d^2\left(2d^2+3d-4\right)$

Explanation of Solution

Given expression: $6d^4+9d^3-12d^2$

Calculation:

The numbers 6,9 and 12 has GCF 3.

Also, the terms $6d^4,9d^3$ and $-12d^2$ has common factor d with exponent 2.

Therefore, GCF of the terms of given expression is $3d^2$ .

Therefore, we can take the GCF of the terms of the expression common out of it as follows.

  $3d^2\left(2d^2+3d-4\right)$

Therefore, the factorized form of given expression is $3d^2\left(2d^2+3d-4\right)$