Question

Given that f(x) = x2 + 10x + 21 and g(x) = x + 3, find f(x) · g(x) and express the result in standard form.

Answer 1

We conclude that:

`f\left(x\right)\cdot g\left(x\right)=x^3+13x^2+51x+63`

Explanation:

Given

`f\left(x\right)=\left(\:x^2\:+\:10x\:+\:21\right)`

`g(x)=x+3`

Determining f(x) · g(x)

`f\left(x\right)\cdot g\left(x\right)=\left(\:x^2\:+\:10x\:+\:21\right)* \left(x+3\right)`

Distribute parentheses

`=x^2x+x^2* \:3+10xx+10x* \:3+21x+21* \:3`

`=x^2x+3x^2+10xx+10* \:3x+21x+21* \:3`

`=x^3+3x^2+10x^2+30x+21x+63`

Add similar elements:
`3x^2+10x^2=13x^2`

`=x^3+13x^2+30x+21x+63`

Add similar elements:
`30x+21x=51x`

`=x^3+13x^2+51x+63`

Therefore, we conclude that:

`f\left(x\right)\cdot g\left(x\right)=x^3+13x^2+51x+63`