Question

what value of k, y^3+2k-2 is exactly divisible by y + 1

Answer 1

Let the given polynomial be p(y) = y^3 + 2k –2.

Since p(y) = y^3 + 2k –2 is exactly divisible by y + 1,

so y+1 = 0

y= -1 is a factor

∴ p (–1)=0 (Factor Theorem)

p(-1) = (-1)^3+2k-2 = 0

= -1+2k-2 = 0

2k-3 = 0

2k = 3

k = 3/2