Factoring by GCF

Question

Find the GCF of the polynomial 32x2y+24x2y2.  Do not factor.

Answer 1

8x^2)y

32=8(4)

24=8(3)

both terms have an x^2

both terms have y as a factor

multiply them together to get 8x^2y

Answer 2

For the number part of the GCF, we need to figure out the greatest number we can divide 32 and 24 by. I get 8.

For the variable part, we pick the variables that are in both terms. I see an x and a y.

Now we figure out which exponent to use for each variable in the GCF. We take the smallest exponent for each variable. So we get x² and y.

That makes the GCF 8x²y.

Answer 3

The given polynomial is 32x²y + 24x²y²

To find the GCF, you need to find the term that has highest number that is a factor of both 32 and 24 and

the variable part with the highest exponent that is a factor of the variable parts in the given binomial.

8 is the greatest factor of 32 and 24.

x² is certainly a factor of both the terms

y is also a factor of both the terms.

So the GCF for the given polynomial is 8x²y.