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

Question

.(2 points)
_ x2+ _ x+ _

Answer 1

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

1. First: Multiply the first terms:
   \(2x \cdot x = 2x^2\)

2. Outer: Multiply the outer terms:
   \(2x \cdot (-4) = -8x\)

3. Inner: Multiply the inner terms:
   \(1 \cdot x = 1x\)

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

Now, combine all of these results:

\[ 2x^2 - 8x + 1x - 4 \]

Combine the like terms \((-8x + 1x)\):

\[ 2x^2 - 7x - 4 \]

So the product of the polynomials is:

\[ 2x^2 - 7x - 4 \]

Filling in the blanks:
_ \(2\) _ \(-7\) _ \(-4\)