Question

if the polynomial (kx³+3x²-13) and (5x³-8x+k) leave the same remainders when divided by x+1, then find the value of k​

Answer 1

K[-1]^3+3[-1]^2-13

-1k+3-13

-1k-10

Put -1 in second value answer will be

3+k

Then,

-1k-10

K+3

Subtract k with k and subtract -10with3

Answer will be k-7=0 then k=7

Answer 2

Answer: -13/2

Step-by-step explanation:

Suppose p(x) = x+1=0

x=-1

According to the factor theorem:-

=> P(-1) = kx^3+3x^2-13 = 5x^3-8x+k

= K(-1)^3+3(-1)^2-13 = 5(-1)^3-

8(-1)+k

= -1k+3-13 = -5+8+k

= -1k-k = -5+8-3+13

= 2k = -13

= K= -13/2 (ans)