If x\(^4\) - kx\(^3\) + 10x\(^2\) + lx - 3 is divisible by (x - 1), and if when it is divided by (x + 2) the remainder is 27, find the constants k and l
A
k = -7, 1 = -15
B
k = -15, 1 = -7
C
k = \(\frac{15}{3}\) , 1 = -7
D
k = \(\frac{7}{3}\) , 1 = -17
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
If k = -7 is put as l = -15, the equation x\(^4\) - kx\(^3\) + 10x\(^2\) + lx - 3 becomes x\(^4\) - (7x\(^3\)) + 10x\(^2\) + (15) -3 = x\(^4\) + 7x\(^3\) + 10x\(^2\) - 15x - 3
This equation is divisible by (x - 1) and (x + 2) with the remainder as 27
k = -7, l = -15
Source: Myschool Past Questions Archive (Record #32723)