Question

if (k+y)is a factor of each polynomial y2 +2y-15 and y3+a find value of a and k

Answer 1

Put (k+y)=0 and then put the value in both polynomials

Answer 2

Answer:

The values of k are 5 and -3. The values of a are 125 and -27.

Step-by-step explanation:

The given polynomials are

$p(y)=y^2+2y-15$

$q(y)=y^3+a$

It is given that (k+y)is a factor of each polynomial P(y) and q(y). It means y=-k is a factor of given polynomials and p(-k)=0, q(-k)=0

$p(-k)=(-k)^2+2(-k)-15$

$0=k^2-2k-15$

$0=k^2-5k+3k-15$

$0=k(k-5)+3(k-5)$

$0=(k-5)(k+3)$

$k=5,-3$

The values of k are 5 and -3.

$q(-k)=(-k)^3+a$

$0=-k^3+a$

$k^3=a$

$(5)^3=a$

$125=a$

$(-3)^3=a$

$-27=a$

Therefore the values of a are 125 and -27.