Question

xpress your answer as a polynomial in standard form.
$f(x) = 2x^2 + 3x - 6$
$g(x) = -4x + 10$
find: $g(f(x))$

Explanation:

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

We know that \( g(x)= -4x + 10 \), so we substitute \( x = f(x)=2x^{2}+3x - 6 \) into \( g(x) \). Then we get \( g(f(x))=-4(2x^{2}+3x - 6)+10 \).

Step2: Distribute the -4

Using the distributive property \( a(b + c + d)=ab+ac + ad \), we have:
\( -4\times2x^{2}+(-4)\times3x+(-4)\times(-6)+10=-8x^{2}-12x + 24 + 10 \)

Step3: Combine like terms

Combine the constant terms \( 24 \) and \( 10 \):
\( -8x^{2}-12x+(24 + 10)=-8x^{2}-12x + 34 \)

Answer:

\( -8x^{2}-12x + 34 \)