Find the value of k if the remainder is -3 when kx^3+8x^2-4x+10 is divided by x+1.

Answer 1

Let us assume f(x) = k x³ + 8 x² - 4 x + 10

d(x) = x +1

q(x) = the quotient

r(x) = the remainder

f(x) / d (x) = q(x) + r(x) / d(x)

f(x) = q(x) d(x) + r(x) [multiply both sides by d(x) ]

k x³ + 8 x² - 4 x + 10 = q(x) (x+1) - 3 ---------(1)

in equation (1) plug - 1 for x,

k ( -1 )³ + 8( -1)² - 4 (-!) + 10 = q(x) ( -1+1) - 3

-k + 8 + 4 + 10 = q( x) * 0 - 3

-k + 22 = - 3

- k = - 3- 22

k= 25

Answer 2

p(x) = q(x) (x-a) + r

p(a) = r

Here a = -1

p(x) is the given function

r = -3

So you have to find k so that p (-1) = -3

So substitute x = -1, then solve for k