Question

What is the product of the polynomials (3x−4)(2x+1)
?(1 point)
Responses

5x2−9x−5
5 x squared minus 9 x minus 5

6x2+12x+4
6 x squared plus 12 x plus 4

6x2−5x−4
6 x squared minus 5 x minus 4

x2+6x−4
x squared plus 6 x minus 4

Answer 1

To find the product of the polynomials \((3x−4)(2x+1)\), we can use the distributive property (also known as the FOIL method for binomials).

1. Multiply the first terms:
\(3x \cdot 2x = 6x^2\)

2. Multiply the outer terms:
\(3x \cdot 1 = 3x\)

3. Multiply the inner terms:
\(-4 \cdot 2x = -8x\)

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

Now, combine these results:

\[
6x^2 + 3x - 8x - 4
\]

Combine like terms (\(3x - 8x\)):

\[
6x^2 - 5x - 4
\]

So, the product of the polynomials \((3x−4)(2x+1)\) is:

**6x² - 5x - 4.**

The correct answer from the options provided is:

**6 x squared minus 5 x minus 4.**