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Math
Charlene Maldonado

The polynomials p(x) = 4x^3– 2x^2+ px+ 5 and g (x) = x^3+ 6x^2+ p leave the remainders a^2and b respectively, when divided by (x+2). Find the value of p if a + b = 0.​

answers: 1
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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

240
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