Question

express your answer as a polynomial in standard form.
$f(x) = x + 2$
$g(x) = 3x^2 + 6x - 8$
find: $g(f(x))$

Explanation:

Step1: Substitute $f(x)$ into $g(x)$

$g(f(x)) = 3(x+2)^2 + 6(x+2) - 8$

Step2: Expand $(x+2)^2$

$(x+2)^2 = x^2 + 4x + 4$, so $3(x^2 + 4x + 4) = 3x^2 + 12x + 12$

Step3: Expand $6(x+2)$

$6(x+2) = 6x + 12$

Step4: Combine all terms

$3x^2 + 12x + 12 + 6x + 12 - 8$

Step5: Simplify like terms

$3x^2 + (12x+6x) + (12+12-8) = 3x^2 + 18x + 16$

Answer:

$3x^2 + 18x + 16$