Question

Find the value of k for which the polynomials p(x)= kx + 3x02 - 13 and g(x) = 2x3 – 5x + k when divided by (x - 2) leave the same remainder.

Answer 1

Step-by-step explanation:Given polynomials are p(x)=kx  

3

+3x  

2

−3 and Q(x)=2x  

3

−5x+k.

It is also given that these two polynomials leave the same remainder when divided by (x−4), therefore, we equate the polynomials and substitute x=4 as shown below:

k(4)  

3

+3(4)  

2

−3=2(4)  

3

−5(4)+k

⇒64k+48−3=128−20+k

⇒64k+45=k+108

⇒64k−k=108−45

⇒63k=63

⇒k=1

Hence, k=1.