Answer:
f(x) = x3 − 3x2 − 13x + 15 Factor: x+3
f(x) = x4 + 3x3 − 8x2 + 5x − 25 Factor: x+5
f(x) = x3 − 2x2 − x + 2 Factor: x-2
f(x) = -x3 + 13x − 12 Factor: x+4
Step-by-step explanation:
f(x) = x^3 − 3x^2 − 13x + 15
Solving:
We will use rational root theorem: -1 is the root of x^3 − 3x^2 − 13x + 15 so, factor out x+1
x^3 − 3x^2 − 13x + 15 / x+1 = x^2-2x-15
Factor: x^2-2x-15 =(x+3)(x-5)
So, factors are: (x+1)(x+3)(x-5)
Factor: (x+5)
f(x) = x^4 + 3x^3 − 8x^2 + 5x − 25
Solving:
We will use rational root theorem: -5 is the root of x^4 + 3x^3 − 8x^2 + 5x − 25, so factour out (x+5)
x^4 + 3x^3 − 8x^2 + 5x − 25 / x+5 = x^3-2x^2 +2x -5
So, factors are (x+5) (x^3-2x^2 +2x -5)
Factor: x+5
f(x) = x^3 − 2x^2 − x + 2
Solving:
x^2(x-2)-1(x-2)
(x-2)(x^2-1)
(x-2) (x-1) (x+1)
Factor: x-2
f(x) = -x^3 + 13x − 12
Solving:
-(x^3 + 13x -12)
We will use rational root theorem:
The 1 is a root of (x^3 + 13x -12) so, factor out x-1
Now solving (x^3 + 13x -12)/x-1 we get (x-3)(x+4)
So, roots are: - (x-1)(x-3)(x+4)
Factor (x+4)
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