Question

if the polynomials (kx cube +3x square - 13) and (5 x cube - 8x + k) leave the same remainders when divided by x + 1,then find the value of k.

Answer 1

Let f(x) = 3x3 - 5x2 + kx - 2 Remainder when f(x) is divided by (x + 2) is f(-2). f(-2) = 3(-2)3 - 5(-2)2 + kx - 2 = -24 - 20 + k(-2) - 2 = -2k - 46 Let g(x) = -x3 -x2 + 7x + k Remainder when g(x) is divided by (x + 2) is g(-2). g(-2) = -(-2)3 - (-2)2 + 7(-2) + k = 8 - 4 - 14 + k = k - 10 According to the question, -2k - 46 = k - 10 -3k = - 10 + 46 -3k = 36 k = -12.

Answer 2

Answer:

x+1=0

x=-1

kx^3+3x^2-13÷x+1=5x^3-8x+k÷x+1

substituting value of x

k(-1) ^3+3(-1) ^2-13=5(-1) ^3-8(-1) +k

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

-k -10=3+k

-13=2k

k=-13/2

Step-by-step explanation:

we equated them because both have same remainders