Question

Choose the expression that shows P(x)=x^3 + 5^2 + 11x + 10 as a product of two factors.

Answer 1

The correct answer is D

Explanation:

You can find the correct answer just by looking at what the first term would end up being.

The first three, if you expanded them, would all have the starting term 2x³, which does not match the result unless the two is factored out. Only the last one would end up with the correct x³ as its first term.

Let's expand it to see if we're right:

(x + 2)(x² + 3x + 5)

= x³ + 3x² + 5x + 2x² + 6x + 10

= x³ + 3x² + 11x + 10

And that's a match, so the correct answer is D

Answer 2

The expression that shows P(x) = x³ + 5x² + 11x + 10 as a product of two factors i (x + 2)(x² + 3x + 5)

To factor the given polynomial
`\(P(x) = x^3 + 5x^2 + 11x + 10\)`, we need to identify the correct factorization among the options provided.

We can expand each factorization to see if it equals the original polynomial P(x):

A.
`\(2x(x^2 + 3x + 3) = 2x^3 + 6x^2 + 6x\)`

B.
`\((x + 1)(2x^2 + 3x + 6) = 2x^3 + 3x^2 + 6x + 2x^2 + 3x + 6 = 2x^3 + 5x^2 + 9x + 6\)`

C.
`\((2x + 3)(x^2 + x + 2) = 2x^3 + 2x^2 + 4x + 3x^2 + 3x + 6 = 2x^3 + 5x^2 + 7x + 6\)`

D.
`\((x + 2)(x^2 + 3x + 5) = x^3 + 3x^2 + 5x + 2x^2 + 6x + 10 = x^3 + 5x^2 + 11x + 10\)`

Among the options, only option D,
`\((x + 2)(x^2 + 3x + 5)\)`, equals the original polynomial P(x). Therefore, the correct answer is **D**.