Question

determine the remainder if the polynomial is divided by the binomial (apply remainder theorem).
$(6x^{3}+30x^{2}+20x - 23)div(x + 4)$
5
-7
7
-5

Explanation:

Step1: Identify root of divisor

Set $x+4=0$, solve for $x$: $x=-4$

Step2: Apply Remainder Theorem

Substitute $x=-4$ into $f(x)=6x^3+30x^2+20x-23$:

$$\begin{align*} f(-4)&=6(-4)^3 + 30(-4)^2 + 20(-4) -23\\ &=6(-64)+30(16)-80-23\\ &=-384+480-80-23 \end{align*}$$

Step3: Calculate final value

$$-384+480=96;\ 96-80=16;\ 16-23=-7$$

Answer:

-7