Given the following:

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

2x4−3x3−12x2+18x
2 x to the 4th power minus 3 x cubed minus 12 x squared plus 18 x

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
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Answer 1

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

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

Now, we calculate \( (f \cdot g)(x) = f(x) \cdot g(x) \): \[ (2x^2 - 3x)(x^2 - 6) \]

We will use the distributive property (also known as the FOIL method for two binomials):

1. Distribute \( 2x^2 \): \[ 2x^2 \cdot x^2 = 2x^4 \] \[ 2x^2 \cdot (-6) = -12x^2 \]

2. Distribute \( -3x \): \[ -3x \cdot x^2 = -3x^3 \] \[ -3x \cdot (-6) = 18x \]

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

Thus, the final expression for \( (f \cdot g)(x) \) is: \[ 2x^4 - 3x^3 - 12x^2 + 18x \]

This matches with the second option from the responses: \[ 2x^4 - 3x^3 - 12x^2 + 18x \]

So, the correct answer is: 2x^4−3x^3−12x^2+18.