Answer:
f(x) = x³ – 3x² – 10x + 24 = (x + 3)(x – 2)(x – 4)
Step-by-step explanation:
I would use the Horner method.
f(x) = x³ – 3x² – 10x + 24
f(2) = 2³ - 3·2² - 10·2 +24 = 0 ⇒ x=2 is the root of function
So:
| 1 | -3 | -10 | 24 |
2 | 1 | -1 | -12 | 0 |
therefore:
f(x) = x³ – 3x² – 10x + 24 = (x – 2)(x² – x – 12)
For x² – x – 12:
[tex]x=\dfrac{1\pm\sqrt{(-1)^2-4\cdot1\cdot(-12)}}{2\cdot1}=\dfrac{1\pm\sqrt{1+48}}{2}=\dfrac{1\pm7}{2}\\\\x_1=\dfrac{1+7}{2}=4\ ,\qquad x_2=\dfrac{1-7}{2}=-3[/tex]
It means:
f(x) = x³ – 3x² – 10x + 24 = (x – 2)(x – 4)(x + 3)
