Question

1. divide.

\frac{x^{2}-6x + 14}{x + 2}
○ x + 4+\frac{14}{x + 2}
○ x-30+\frac{5}{x + 2}
○ x + 6-\frac{32}{x + 2}
○ x-8+\frac{30}{x + 2}

Explanation:

Step1: Use polynomial long - division

We divide $x^{2}-6x + 14$ by $x + 2$. First, divide the leading term of the dividend $x^{2}-6x + 14$ (which is $x^{2}$) by the leading term of the divisor $x+2$ (which is $x$). $\frac{x^{2}}{x}=x$.

Step2: Multiply and subtract

Multiply $x + 2$ by $x$ to get $x^{2}+2x$. Then subtract this from the dividend: $(x^{2}-6x + 14)-(x^{2}+2x)=x^{2}-6x + 14 - x^{2}-2x=-8x + 14$.

Step3: Repeat the process

Divide the leading term of $-8x + 14$ (which is $-8x$) by the leading term of $x + 2$ (which is $x$). $\frac{-8x}{x}=-8$.

Step4: Multiply and find the remainder

Multiply $x + 2$ by $-8$ to get $-8x-16$. Subtract this from $-8x + 14$: $(-8x + 14)-(-8x-16)=-8x + 14 + 8x+16 = 30$.
So, $\frac{x^{2}-6x + 14}{x + 2}=x-8+\frac{30}{x + 2}$.

Answer:

$x-8+\frac{30}{x + 2}$ (the last option)