Question

check if the polynomial p(y)= 8y^3+4y^2 -y-3 is a multiple of (2y+3)​

Answer 1

Step-by-step explanation:

(2y+3) =>factor.

y= -3/2=>zero of the polynomial.

Substituting the zero in the given polynomial.

p(y)=8y^3+4y^2-y-3.

p(-3/2)=8(-3/2)^3 +4(-3/2)^2 -(-3/2)-3.

          =8(-27/8) +4(9/4) +(3/2)-3.

          = -27 +9 +(3/2)-3             {LCM=2}

          = (-54+18+3-6)/2

          = -39/2

          = -19.5 $\neq$0.

Hence (2y+3) isn't a factor of  p(y) and therefore the given polynomial is not a multiple of (2y+3).