Question

13 divide using long or synthetic division.
$-14x^3 + 14x - 840$ by $(x + 4)$
a $14x^2 + 56x - 238 + \frac{1680}{x + 4}$
b $-14x^2 - 56x + 238 - \frac{1680}{x + 4}$
c $14x^2 - 56x + 210$
d $-14x^2 + 56x - 210$

Explanation:

Step1: Use Synthetic Division

The divisor is \(x + 4\), so the root is \(x=-4\). The polynomial is \(-14x^{3}+0x^{2}+14x - 840\) (we add the missing \(x^{2}\) term with coefficient 0).
Set up synthetic division:

$$
LATEXBLOCK0
$$

Step2: Interpret the Result

The coefficients from synthetic division give the quotient polynomial. The first three numbers are the coefficients of \(x^{2}\), \(x\), and the constant term, and the last number is the remainder (which is 0 here). So the quotient is \(-14x^{2}+56x - 210\) with a remainder of 0.

Answer:

D. \(-14x^{2}+56x - 210\)