Question

Find K if 4 x square - 2 X square + kx + 5 leaves a remainder -10 when divided by 2x+1​

Answer 1

`k = 31`

Explanation:

Given

`f(x) = 4x^2 - 2x^2 + kx + 5`

`r = -10` --- remainder

`d = 2x + 1` --- divisor

Required

Find k

We have:

`d = 2x + 1` --- divisor

Equate to 0

`2x + 1 = 0`

Solve for x

`2x = -1`

`x =-0.5`

This means that:

`f(-0.5)=-10`

So, we have:

`4*(-0.5)^2 - 2*(-0.5)^2 + k*-0.5 + 5 =-10`

`0.5 -0.5k + 5 =-10`

Collect like terms

`-0.5k=-10-5-0.5`

`-0.5k=-15.5`

Solve for k

`k = -15.5/-0.5`

`k = 31`