Question

Question 2(Multiple Choice Worth 2 points)
(02.02 MC)

Select one of the factors of x3y2+ 8xy2 + 5x2 + 40.

(xy2 + 5)
(x2 + 4)
(xy2 − 5)
(x2 − 8)

Answer 1

To factor the expression \(x^3y^2 + 8xy^2 + 5x^2 + 40\), we can rearrange it as follows:

\[
x^3y^2 + 5x^2 + 8xy^2 + 40
\]

Group the terms in pairs:

\[
(x^3y^2 + 5x^2) + (8xy^2 + 40)
\]

Now we can factor each pair:

1. From the first pair \(x^3y^2 + 5x^2\), we can factor out \(x^2\):

\[
x^2(xy^2 + 5)
\]

2. From the second pair \(8xy^2 + 40\), we can factor out 8:

\[
8(xy^2 + 5)
\]

Now, we can combine these:

\[
x^2(xy^2 + 5) + 8(xy^2 + 5) = (xy^2 + 5)(x^2 + 8)
\]

Looking through the answer choices provided, we can select the factor \(xy^2 + 5\) as it corresponds to one of the factored components:

1. (xy² + 5) ✅
2. (x² + 4)
3. (xy² − 5)
4. (x² − 8)

Thus, the correct answer is:

**(xy² + 5)**.