Question

Multiply the polynomials (3x−1)(2x+4)
(
3
𝑥
−
1
)
(
2
𝑥
+
4
)
.(2 points)
x2+
𝑥
2
+
x+
𝑥
+

Answer 1

To multiply the polynomials \((3x - 1)(2x + 4)\), we can use the distributive property (often referred to as the FOIL method for binomials).

Let's distribute each term in the first polynomial to each term in the second polynomial:

1. Multiply \(3x\) by \(2x\):
\[
3x \cdot 2x = 6x^2
\]

2. Multiply \(3x\) by \(4\):
\[
3x \cdot 4 = 12x
\]

3. Multiply \(-1\) by \(2x\):
\[
-1 \cdot 2x = -2x
\]

4. Multiply \(-1\) by \(4\):
\[
-1 \cdot 4 = -4
\]

Now we combine all the results:
\[
6x^2 + 12x - 2x - 4
\]

Combine like terms (the \(12x\) and \(-2x\)):
\[
6x^2 + (12x - 2x) - 4 = 6x^2 + 10x - 4
\]

So, the product of the polynomials \((3x - 1)(2x + 4)\) is:
\[
\boxed{6x^2 + 10x - 4}
\]