Question

Given one factor of the polynomial, factor the polynomial completely.

f(x) = x^3 - 4x^2 - 7x + 10; X - 5​

Answer 1

The factors are (x - 1)(x - 5)(x + 2).

Explanation:

Long division:

x - 5 )x^3 - 4x^2 - 7x + 10( x^2 + x - 2 <--------- Quotient.

x^3 - 5x^2

x^2 - 7x

x^2 - 5x

- 2x + 10

-2x + 10

...........

x^ 2 + x - 2 = (x + 2)(x - 1).