Question

Multiply the polynomials:
(x + 2) (x^2 - 7x + 4)

Answer 1

To multiply the polynomials \((x + 2)(x^2 - 7x + 4)\), we will use the distributive property (also known as the FOIL method for binomials).

1. Distribute \(x\) across the second polynomial \((x^2 - 7x + 4)\):
\[
x \cdot (x^2 - 7x + 4) = x^3 - 7x^2 + 4x
\]

2. Distribute \(2\) across the second polynomial \((x^2 - 7x + 4)\):
\[
2 \cdot (x^2 - 7x + 4) = 2x^2 - 14x + 8
\]

3. Now, combine the results from the two distributions:
\[
(x^3 - 7x^2 + 4x) + (2x^2 - 14x + 8)
\]

4. Combine like terms:
\[
x^3 + (-7x^2 + 2x^2) + (4x - 14x) + 8
\]
\[
= x^3 - 5x^2 - 10x + 8
\]

Thus, the product of the polynomials \((x + 2)(x^2 - 7x + 4)\) is:
\[
\boxed{x^3 - 5x^2 - 10x + 8}
\]