If x4 - kx3 + 10x2 + 1x - 3 is divisible by (x - 1), and if when it is divided by (x + 2) the remainder is 27, find the constants k and 1
A. k = -7, 1 = -15 B. k = -15, 1 = -7 C. k = \(\frac{15}{3}\) , 1 = -7 D. k = \(\frac{7}{3}\) , 1 = -17
Correct Answer: A
Explanation
If k = -7 is put as -15, the equation x4 - kx3 + 10x2 + 1x - 3 becomes x4 - (7x3) + 10x2 + (15)-3 = x4 + 7x3 + 10x2 - 15x - 3 This equation is divisible by (x - 1) and (x + 2) with the remainder as 27 k = -7, 1 = -15
