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
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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: Option 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