Question

(x+1)(4x^2+7x+6)

multiply the polynomials

Answer 1

To multiply the polynomials \((x + 1)(4x^2 + 7x + 6)\), we will distribute each term in the first polynomial \((x + 1)\) to every term in the second polynomial \((4x^2 + 7x + 6)\).

Let's do the multiplication step by step:

1. Multiply \(x\) by each term in \(4x^2 + 7x + 6\):
\[
x \cdot 4x^2 = 4x^3
\]
\[
x \cdot 7x = 7x^2
\]
\[
x \cdot 6 = 6x
\]

2. Next, multiply \(1\) by each term in \(4x^2 + 7x + 6\):
\[
1 \cdot 4x^2 = 4x^2
\]
\[
1 \cdot 7x = 7x
\]
\[
1 \cdot 6 = 6
\]

3. Now combine all of those results:
\[
4x^3 + 7x^2 + 6x + 4x^2 + 7x + 6
\]

4. Combine like terms:
- The \(x^2\) terms: \(7x^2 + 4x^2 = 11x^2\)
- The \(x\) terms: \(6x + 7x = 13x\)

Putting it all together, we get:
\[
4x^3 + 11x^2 + 13x + 6
\]

Thus, the product of the polynomials \((x + 1)(4x^2 + 7x + 6)\) is:
\[
\boxed{4x^3 + 11x^2 + 13x + 6}
\]