Question

(x-5) is a factor of the polynomial p(x) = 2X3power -5X2power-28x+15

Answer 1

To check if (x-5) is a factor of the polynomial 2x³ - 5x² - 28x + 15,
First equate x-5 to 0 and find value of x.
x -  = 0
⇒ x = 5
If x=5 is a root of the polynomial, then (x-5) is a factor.

at x=5, value of polynomial is
2×(5)³ - 5×(5)² - 28×(5) + 15,
= 2×125 - 5×25 - 28×5 + 15
= 250 - 125 - 140 + 15
= 265 - 265
= 0
So 5 is a root of the polynomial.
Thus (x-5) is a factor of the polynomial.