Question

The polynomial p(x) = kx +98 +4x-8 when divided by x+ 3 leaves a reminder - 20. find the value of k​

Answer 1

Answer:

Value of k = 3

Step-by-step explanation:

By Remainder Theorem:

If p(x) is any polynomial of degree greater than or equal to 1 and p(x) is divided by the linear polynomial (x-a) ,then the remainder is p(a).

Here ,

p(x) = kx³+9x²+4x-8 is divided by (x+3) .

Remainder =p(-3)

But , Remainder = 10(1-k)

/* given */

=> p(-3)=10(1-k)

=> k(-3)³+9(-3)²+4(-3)-8=10-10k

=> -27k+81-12-8=10-10k

=> 81-20-10=27k-10k

=> 51=17k

Divide each term by 17, we get

=> 3 = k

Therefore,

Value of k = 3