Question

Find the product of the polynomials (2x + 1) (x + 4)
_x^2+_x+_

Answer 1

To find the product of the polynomials \( (2x + 1)(x + 4) \), we can use the distributive property (also known as the FOIL method for two binomials).

1. Multiply the first terms:
\[ 2x \cdot x = 2x^2 \]

2. Multiply the outer terms:
\[ 2x \cdot 4 = 8x \]

3. Multiply the inner terms:
\[ 1 \cdot x = 1x \]

4. Multiply the last terms:
\[ 1 \cdot 4 = 4 \]

Now, we combine all these results:
\[
2x^2 + 8x + 1x + 4 = 2x^2 + (8x + 1x) + 4
\]
\[
= 2x^2 + 9x + 4
\]

Thus, the product of the polynomials \( (2x + 1)(x + 4) \) is:
\[
\boxed{2x^2 + 9x + 4}
\]