Question

question
express your answer as a polynomial in standard form.
$f(x)=3x^2+6x+14$
$g(x)=x-6$
find: $f(g(x))$

Explanation:

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

Replace $x$ in $f(x)$ with $x-6$:
$f(g(x)) = 3(x-6)^2 + 6(x-6) + 14$

Step2: Expand $(x-6)^2$

Use $(a-b)^2=a^2-2ab+b^2$:
$(x-6)^2 = x^2 - 12x + 36$
$f(g(x)) = 3(x^2 - 12x + 36) + 6(x-6) + 14$

Step3: Distribute coefficients

Multiply terms inside parentheses:
$f(g(x)) = 3x^2 - 36x + 108 + 6x - 36 + 14$

Step4: Combine like terms

Group and simplify similar terms:
$f(g(x)) = 3x^2 + (-36x+6x) + (108-36+14)$
$f(g(x)) = 3x^2 - 30x + 86$

Answer:

$3x^2 - 30x + 86$