Question

If f(x) = x2 − x − 12 and g(x) = x2 − 16, find f(x) × g(x).

Answer 1

Answer:
`f(x)*g(x)=x^4-x^3-28x^2+16x+192`

Explanation:

Given the function f(x) and g(x):

`f(x)=x^2 - x -12\\\\g(x)= x^2 - 16`

We need to multiply them. To do this we need to remember the Product of power property, which states:

`(a^m)(a^n)=a^((m+n))`

And the multiplication of signs:

`(+)(+)=+\\(+)(-)=-\\(-)(-)=+`

Then:

`f(x)*g(x)=(x^2 - x -12)(x^2 - 16)\\\\f(x)*g(x)=x^4-16x^2-x^3+16x-12x^2+192`

Adding like terms, we get:

`f(x)*g(x)=x^4-x^3-28x^2+16x+192`

Answer 2

f(x) × g(x)= x^4 - x^3 - 28x^2 + 16x + 192

Explanation:

We have the function f(x) = x^2 − x − 12 and g(x) = x^2 − 16 and we need to find the multiplication of both functions.

f(x) × g(x) = ( x^2 − x − 12)(x^2 − 16) = x^4 - 16x^2 -x^3 + 16x -12x^2 + 192

Simplifying:

f(x) × g(x)= x^4 - x^3 - 28x^2 + 16x + 192