Question

Find the value of p when 4 x^3 + 4^2 + px + 6 is divided by 2x-3 leaving a remainder -12.​
pls help answer is not in​

Answer 1

Remainder theorem:

When we divide f(x)f(x) by (x−c)(x−c) , the remainder f(c)f(c)

When  p(x)=4x3−2x2+px+5p(x)=4x3−2x2+px+5  is divided by (x+2)(x+2), the remainder is

p(−2)=4(−2)3−2(−2)2+p(−2)+5p(−2)=4(−2)3−2(−2)2+p(−2)+5

=−2p−35=−2p−35

So,

a=−2p−35a=−2p−35

When  q(x)=x3+6x2+pq(x)=x3+6x2+p  is divided by (x+2)(x+2), the remainder is

q(−2)=(−2)3+6(−2)2+pq(−2)=(−2)3+6(−2)2+p

=p+16=p+16

So,

b=p+16b=p+16

Now

a+b=0a+b=0

−2p−35+p+16=0−2p−35+p+16=0

−p−19=0−p−19=0

P=-19

Answer 2

Answer:

c) -27 is the correct answer