Answer:
See below in bold.
Step-by-step explanation:
The first one looks like x + 3 might be a factor. By the Factor Theorem :To check we plug in x = -3 to see if the f(3) = 0.
f(3) = -27 - 27 + 39 + 15 = 0
So x+3 is a factor of x^3 - 3x^2 - 13x + 15.
x^3 - 2x^2 - x + 2
Because of the last term +2 , it looks like x - 2 might be a factor of this so we evaluate f(2)
f(2) = 8 - 8 - 2 + 2 = 0
So x - 2 is a factor of x^3 - 2x^2 - x + 2 .
x^4 + 3x^3 - 8x^2 + 5x - 25.
Because of the - 25 x + 5 could be a factor so try f(-5)
= (-5)^4 - 3* -125 - 8*25 + 5 * -5 - 25 = 0
So x + 5 is a factor of x^4 + 3x^3 - 8x^2 + 5x - 25.
Finally we check if (x + 4) is a factor of -x^3 + 13x - 12 :
f(-4) = - (-4)^3 + 13*-4 - 12 = 0.
So x + 4 is a factor of -x^3 + 13x - 12.
