Factor x2 – 8x + 15. Which pair of numbers has a product of ac and a sum of b?

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Question:

Factor x2 – 8x + 15. Which pair of numbers has a product of ac and a sum of b?

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Answer:

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.

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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:

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