Verified Answer :

isyllus

Answer:

Pair of numbers: -3 and -5

Factors : (x-5)(x-3)

Step-by-step explanation:

Given: \(x^2-8x+15\)

We need to factor it using AC method.

For equation: \(ax^2+bx+c\)

For factor this ac and sum b

For our equation: a=1, b=-8 and c=15

Therefore,

Product = ac = (1)(15) = 15

We need to choose two number whose product is 15 and sum -8

First we find all the factor of 15: 1x15    3x5    

If we take 3x5

Product:  (-3)(-5) = 15

Sum:          -3-5  = -8

Pair of numbers: (-3,-5)

Now we will factor it.

\(\Rightarrow x^2-8x+15\)

\(\Rightarrow x^2-5x-3x+15\)

\(\Rightarrow (x^2-5x)+(-3x+15)\)

\(\Rightarrow x(x-5)-3(x-5)\)

\(\Rightarrow (x-5)(x-3)\)

The factors are (x-5) and (x-3)

ajeigbeibraheem

The pair of numbers that has a product of ac and a sum of b is (x - 5) (x -3.)

What is a quadratic equation?

A quadratic equation is used for the expression of algebraic terms in their second degree. It is used written in the form:

  • ax² + bx + c = 0

From the given  information:

  • x² - 8x + 15 = 0

where;

  • a = 1
  • b =  - 8
  • c = 15

To determine the product of ac and the sum of b;

We will look for two values that when we multiply them together, we will have +15 and when we add them together we will have -8.

The two values are -3 and - 5

  • The product of -3 and - 15 is ac = +15
  • The sum of -3 and -5 is b = -8

Now, the quadratic equation becomes:
x² - 3x  - 5x + 15 = 0

x(x -3) -5(x -3) = 0

(x -5) (x - 3) = 0

Learn more about quadratic equations here:

https://brainly.com/question/1214333

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