Question

f(x)=2x2−3x


g(x)=x2−6


What is (f⋅g)(x)
?

(1 point)
Responses

3x2−x−6
3 x squared minus x minus 6

2x4+3x3+2x2−18
2 x to the 4th power plus 3 x cubed plus 2 x squared minus 18

−13x9+18x
negative 13 x to the 9th power plus 18 x

2x4−3x3−12x2+18x

Answer 1

To find \((f \cdot g)(x)\), we need to multiply the functions \(f(x)\) and \(g(x)\):

Given:
\[
f(x) = 2x^2 - 3x
\]
\[
g(x) = x^2 - 6
\]

The product \((f \cdot g)(x)\) is computed as follows:
\[
(f \cdot g)(x) = f(x) \cdot g(x) = (2x^2 - 3x)(x^2 - 6)
\]

Now, we will use the distributive property (also known as the FOIL method) to multiply these two polynomials:

1. Multiply \(2x^2\) by each term in \(g(x)\):
\[
2x^2 \cdot x^2 = 2x^4
\]
\[
2x^2 \cdot (-6) = -12x^2
\]

2. Multiply \(-3x\) by each term in \(g(x)\):
\[
-3x \cdot x^2 = -3x^3
\]
\[
-3x \cdot (-6) = 18x
\]

Now, combine all these terms together:
\[
(f \cdot g)(x) = 2x^4 - 3x^3 - 12x^2 + 18x
\]

The final result is:
\[
2x^4 - 3x^3 - 12x^2 + 18x
\]

Thus, the answer is:
\[
\boxed{2x^4 - 3x^3 - 12x^2 + 18x}
\]