Determine the value of k

Question

x²-3x+2k is divided by x+2 the reminder is 7.Without dividing,determine the value of k

Answer 1

Given the fact that x² - 3x + 2k is divisible by x+2 with remainder 7 we can write this equation as

x² - 3x + 2k / (x + 2) = f(x) + 7/(x + 2)

Therefore x² - 3x + 2k = f(x)*(x+2) + 7.

We also know that f(x) is at best a linear function of the for ax+b...

x² - 3x + 2k = (ax+b)(x+2) + 7

x² - 3x + 2k = ax² + (2a + b)x + 2b + 7

Matching like coefficients --> a = 1, 2a+b = -3, 2b + 7 = 2k

a = 1

2 + b = -3 --> b = -5

-10 + 7 --> 2k --> k = -3/2