Question

When x2 + ax + 5 is divided by x − 2, the remainder is 1.What is the value of a?

Answer 1

Answer:

Step-by-step explanation:

According to the Remainder theorem, when a polynomial p(x) is divided by (x−a), then the remainder is the value of p(x) at x=a

Here p(x)=x  

3

+8x  

2

+17x+ax

When it is divided by (x+2),  

Remainder is =p(−2)

=(−2)  

3

+8(−2)  

2

+17(−2)+a(−2)

=−8+32−34−2a

=−10−2a

When it is divided by (x+1),  

Remainder is =p(−1)

=(−1)  

3

+8(−1)  

2

+17(−1)+a(−1)

=−1+8−17−a

=−10−a

Now, both remainders are equal.

−10−2a=−10−a

−2a+a=0

−a=0

a=0