Question

Factor the GCF: 6x4y3 + 21x3y2 − 9x2y.

Answer 1

Answer: Second option :

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

Step-by-step explanation:

Given expression $6x^4y^3+21x^3y^2-9x^2y$.

We need to find greatest common factor (GCF) of all the terms.

Let us write all terms in expanded form first.

$6x^4y^3 = 2 \times 3 \times x \times x \times x \times x \times y \times y \times y$

$21x^3y^2 = 3 \times 7 \times x \times x \times x \times y \times y.$

$9x^2y=3 \times 3 \times x \times x \times y.$

We can see that first factor is 3 common, second factor is $x \times x$ and third factor is y.

Therefore, GCF would be $3x^2y.$

Now, let us factor out GCF $3x^2y$ and keep the remaining terms inside parenthesis.

=$3x^2y(2x^2y^2+7xy -3)$

Therefore, correct option is 2nd option $3x^2y(2x^2y^2+7xy -3)$.