Question

P(x)=x^3+5x^2+2x-8 which three factors of the polynomail

Answer 1

Answer:

(x - 1)(x + 2)(x + 4).

Step-by-step explanation:

p(x)=x^3+5x^2+2x-8

p(1) = 1^3 + 5(1)^2 + 2(1) - 8

= 1 + 5 + 2 - 8 = 0, therefore (x - 1) is a factor  (By the Factor Theorem).

Divide p(x) by x - 1:

      x^2  + 6x + 8   <-------- is the quotient

x - 1 ) x^3 + 5x^2 + 2x - 8

        x^3 - x^2

                 6x^2 + 2x

                  6x^2 - 6x

                              8x - 8

                              8x - 8

                              ............

and x^2 + 6x + 8

= (x + 2)(x + 4).