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Two is a zero of the equation x3−x2−14x+24=0. Which factored form is equivalent to the equation?

A: (x−3)(x−2)(x+4)=0
B: (x−3)(x+2)(x+4)=0
C: (x+4)(x−-√2)(x+-√2)=0
D: (x−2)(x+2)(x+4)=0

Respuesta :

joseaaronlara

Answer:

The answer to your question is: letter A

Step-by-step explanation:

                                             x³ - x² - 14x + 24 = 0

If two is a zero of the polynomial, then x = 2, divide the polynomial by 2.

Synthetic division

                                   1   - 1   - 14   + 24     2

                                         2      2    -24                                

                                   1     1     -12         0

Result                          x² + x - 12 = 0

Factor the polynomial, find two numbers that multiply gives  -12 and added gives + 1.

These numbers are + 4 and - 3

                                 +4 - 3 = +1

                                 (+4)(-3) = -12

                                 (x + 4) (x - 3) = 0

Finally

                              (x +4)(x - 3)(x -2) = 0