Respuesta :

calculista

Answer:

The other factor is [tex](x+2)[/tex]

Step-by-step explanation:

we know that

[tex](x-a)(x-b)=x^{2}-xb-xa+ab[/tex]

[tex](x-a)(x-b)=x^{2}-(a+b)x+ab[/tex]

In this problem we have

[tex]x^{2} -8x-20[/tex]

and

[tex]a=10[/tex] -----> because is a factor

substitute and solve for b

[tex]x^{2} -8x-20=x^{2}-(10+b)x+10b[/tex]

so

[tex]8=10+b\\b=-2[/tex]

Verify in the second equation

[tex]-20=10b[/tex] -----> [tex]-20=10(-2)[/tex] -----> [tex]-20=-20[/tex]--> is ok

The other factor is [tex](x+2)[/tex]

Lanuel

The other factor of the given quadratic equation is equal to x + 2.

Given the following data:

  • Factor = x - 10
  • Quadratic equation = [tex]x^2 -8x -20[/tex]

To calculate the other factor of the given quadratic equation:

How to solve a quadratic equation.

In this exercise, you're required to solve for other factor of a quadratic equation. Thus, we would simplify the expression by applying the perfect-square trinomial.

The perfect-square trinomial.

Mathematically, the perfect-square trinomial is given by this expression:

[tex](x-a)(x-b)=x^2-(a-b)x -ab[/tex]

Comparing the expressions, we have:

  • a = 10

Next, we would solve for b:

[tex]x^2 -8x -20=x^2 -(10+b)x-10b\\\\8=10+b\\\\b=-10+8[/tex]

b = -2.

Substituting the value of b, we have:

Factor = x + 2.

Read more on quadratic equation here: https://brainly.com/question/13170908

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