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: $$\boxed{{\displaystyle 2x^2+9x+4}}$$