Question

when $4x^4 - 13x^2 - 2x + 1$ is divided by $(x + 2)$, what is the remainder

Explanation:

Step1: Apply Remainder Theorem

Set divisor $x+2=0$, get $x=-2$.

Step2: Substitute $x=-2$ into polynomial

$4(-2)^4 -13(-2)^2 -2(-2)+1$

Step3: Calculate each term

$4(16) -13(4) +4 +1 =64 -52 +4 +1$

Step4: Compute result

$64-52=12$, $12+4=16$, $16+1=17$? Wait correction: Wait $4(-2)^4=4*16=64$, $-13(-2)^2=-13*4=-52$, $-2(-2)=4$, $+1$. So $64-52+4+1=17$? Wait no mistake earlier: yes 64-52=12, +4=16, +1=17. So remainder is 17.

Corrected Answer: 17

Step1: Find root of divisor

$x+2=0 \Rightarrow x=-2$

Step2: Substitute $x=-2$ into polynomial

$4(-2)^4 -13(-2)^2 -2(-2)+1$

Step3: Calculate each term

$4×16=64$, $-13×4=-52$, $-2×(-2)=4$, $+1$

Step4: Sum terms

$64-52+4+1=17$

Answer:

3