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Two is a zero of the equation x^3−x^2−14x+24=0.

Which factored form is equivalent to the equation?

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


THE ANSWER IS
C ) (x-3)(x-2)(x+4)=0
trust me on this.

Two is a zero of the equation x3x214x240 Which factored form is equivalent to the equation A x4x2x20 B x2x2x40 C x3x2x40 D x3x2x40 THE ANSWER IS C x3x2x40 trust class=

Respuesta :

Answer:

The factored form is equivalent to the given equation is (x - 2) (x - 3) (x + 4).

Step-by-step explanation:

Since 2 is a zero of the equation [tex]x^{3} - x^{2} -14x + 24 = 0[/tex]

Therefore, (x - 2) is a factor of the equation [tex]x^{3} - x^{2} -14x + 24 = 0[/tex]

Now, on dividing [tex]x^{3} - x^{2} -14x + 24 = 0[/tex] by (x - 2) we get,

[tex](x - 2) (x^{2} + x - 12)[/tex] as shown in Fig(1)

On factorising x² + x - 12

= x² + x - 12

=  x² + 4x - 3x - 12

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

= (x - 3) (x + 4)

Now, [tex](x - 2) (x^{2} + x - 12)[/tex] = [tex](x - 2) (x -3) (x + 4)[/tex]

So the factored form is equivalent to the given equation is (x - 2) (x - 3) (x + 4). Therefore option (c) is the correct answer.

           

       

                 

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abidemiokin

The factored form of the polynomial will be [tex](x-2)(x+4)(x-3)[/tex]

Given the polynomial function [tex]x^3-x^2-14x+24=0.[/tex]

if 2 is a zero of the function, it means that (x-2) is a factor.

Dividing the polynomial function [tex]x^3-x^2-14x+24=0[/tex] by x - 2 will give:

[tex]\frac{x^3-x^2-14x+24}{x-2} =x^2-x+12[/tex]

Cross multiplying;

[tex]x^3-x^2-14x+24 =(x-2)(x^2+x-12)\\x^3-x^2-14x+24 =(x-2)(x^2+4x-3x-12\\x^3-x^2-14x+24 =(x-2)(x(x+4)-3(x+4)\\x^3-x^2-14x+24 =(x-2)(x+4)(x-3)\\[/tex]

This shows that the factored form of the polynomial will be [tex](x-2)(x+4)(x-3)[/tex]

Learn more here: https://brainly.com/question/21121937

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