Question

Choose the expression that shows P(x) = 2x^3 + 5x^2 + 5x + 6 as a product of two factors.

a) 2x(x^2 + 3x + 3)
b) (x+1)(2x^2 + 3x + 6)
c) (x+2)(2x^2 + x + 3)

Answer 1

The expression that shows P(x) = 2x^3 + 5x^2 + 5x + 6 as a product of two factors is option b) (x+1)(2x^2 + 3x + 6).

Step-by-step explanation:

The expression that shows P(x) = 2x^3 + 5x^2 + 5x + 6 as a product of two factors is option b) (x+1)(2x^2 + 3x + 6).

To check if this is the correct answer, we can use the distributive property to expand the expression:

P(x) = (x+1)(2x^2 + 3x + 6)

By multiplying each term in the first factor by each term in the second factor, we get:

P(x) = 2x^3 + 3x^2 + 6x + 2x^2 + 3x + 6

Combining like terms, we have:

P(x) = 2x^3 + 5x^2 + 5x + 6

As you can see, the expanded expression matches P(x), confirming that option b) is the correct factorization.