Question

The remainder when p(x) is divided by x−3 is −2.B. −2=p(3)=(3+(−2))q(3)+0
−2=(3−2)q(3)
−2=(−1)q(3)

Answer 1

Answer:

the answer is -2=(3-2)q(3)

Explanation:

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Answer 2

ANSWER
Remainder theorem:
When we divide f(x) by (x−c) , the remainder f(c)

When p(x)=4x
3
−2x
2
+px+5 is divided by (x+2), the remainder is

p(−2)=4(−2)
3
−2(−2)
2
+p(−2)+5

=−2p−35

So,
a=−2p−35


When q(x)=x
3
+6x
2
+p is divided by (x+2), the remainder is

q(−2)=(−2)
3
+6(−2)
2
+p

=p+16

So,
b=p+16

Now
a+b=0
−2p−35+p+16=0
−p−19=0
p=−19