Question

Factor –7x3 + 21x2 + 3x – 9 by grouping. What is the resulting expression?

Answer 1

Answer:

$(-7x^2+3)(x-3)$

Step-by-step explanation:

To factor by grouping, take the first two numbers and last two numbers.  First, look at the first two numbers.

$-7x^3+21x^2$

Each number can be divided by 7 and x^2, so pull it out as a GCF.

$-7x^3+21x^2 = -7x^2(x-3)$

Next, look at the last two numbers.

$3x-9$

Each number can be divided by 3, so we will pull it out as a GCF.

$3x-9=3(x-3)$

Add the two results together.

$-7x^2(x-3)+3(x-3)$

When factoring by grouping, the two expressions in the parenthesis should always be the same.  In this case, it is x-3.

Combine the numbers outside and inside parenthesis.

$(-7x^2+3)(x-3)$