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

Answer:

We conclude that:

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

Step-by-step explanation:

Given

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

$g(x)=x+3$

Determining f(x) · g(x)

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

Distribute parentheses

                 $=x^2x+x^2\times \:3+10xx+10x\times \:3+21x+21\times \:3$

                 $=x^2x+3x^2+10xx+10\times \:3x+21x+21\times \:3$

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

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:

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