Question

If x + k is the GCD of x2 _ 2x _ 15 and x3+ 27, find the value of k..

Answer 1

Answer:

Here is the solution of your asked query:

Since (x+k) is the GCD of (x2−2x−15) and (x3+27)This means x=−k is zero of both given polynomials.So we have;(−k)2−2(−k)−15=0⇒k2+2k−15=0⇒k2+5k−3k−15=0⇒k(k+5)−3(k+5)=0⇒(k−3)(k+5)=0⇒k=3 and k=−5

Answer 2

(x+k) means x=-k  

x2-2x-15

(-k)2-2(-k)-15=0

k2+2k-15=0

k2+5k-3k-15=0

k(k+5)-3(k+5)

(k-3) (k+5)

k=3, -5

x3+a

(-k)3+a

a=k

a = 27 , -125