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

Question

_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: \[ \boxed{2x^2 + 9x + 4} \]