Question

if $g(x) = x^2 + 9x + 21$ and $h(x) = 2(x + 5)^2$, which is equivalent form of $h(x) - g(x)$?

a $k(x) = x + 4$

b $k(x) = x^2 + 7x + 11$

c $k(x) = x^2 + 11x + 29$

d $k(x) = -x^2 - 11x - 29$

Explanation:

Step1: Expand $h(x)$

$$\begin{align*} h(x)&=2(x+5)^2\\ &=2(x^2+10x+25)\\ &=2x^2+20x+50 \end{align*}$$

Step2: Compute $h(x)-g(x)$

Substitute $g(x)=x^2+9x+21$:

$$\begin{align*} h(x)-g(x)&=(2x^2+20x+50)-(x^2+9x+21)\\ &=2x^2+20x+50-x^2-9x-21 \end{align*}$$

Step3: Combine like terms

$$\begin{align*} h(x)-g(x)&=(2x^2-x^2)+(20x-9x)+(50-21)\\ &=x^2+11x+29 \end{align*}$$

Answer:

C. $k(x) = x^2 + 11x + 29$