Question

Determine whether $(x - 5)$ is a factor of the polynomial $p_{(x)}= 2 x^3 - 5 x^2 - 28 x + 15$.

Answer 1

Substitute x=5 in the polynomial
P(x)= 2(5)³ -5(5)²-28(5)+15
      =2(125)-5(25)-140+15
      = 250-125-140+15
      = 0
hence x-5 is  a factor.

Answer 2

let x-5=0
therefore x=5;
therefore;
P(5)=2(5)³-5(5)²-28(5)+15
=2*125-5*25-28*5+15
=250-125-140+15
=125-140+15
=-15+15=0
hence; x-5 is a factor of P(x).