Find the polynomials (2x+1) (x-4)

Answer 1

To find the polynomial resulting from multiplying $(2x+1)(x-4)$, we can use the distributive property (also known as the FOIL method for 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:
   $1\cdot x=1x$ (or just $x$)

4. Multiply the last terms:
   $1\cdot (-4)=-4$

Now we combine all these results together:
$$2x^2-8x+x-4$$

Next, we combine like terms: $$2x^2-7x-4$$

Thus, the product of the polynomials $(2x+1)(x-4)$ is: $$\boxed{{\displaystyle 2x^2-7x-4}}$$