Question

find the value of a when g(x)is a factor of p(x) g (x)=x+2 ; p(x)=2x² +6x+a​

Answer 1

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