Algebra

Factor: x² - 9x + 20

Step-by-step solution with explanation

Final Answer

(x - 4)(x - 5)

Step-by-step solution

Identify the parts of the quadratic

We have a quadratic in the form where , , and . We need to find two numbers that multiply to give us 20 and add up to give us -9.

List factor pairs of 20

, ,

We write out all the ways to multiply two whole numbers to get 20. Since our constant term is positive and our middle term is negative, we need both factors to be negative.

Find the pair that adds to -9

and

We check each pair to see which one adds up to -9. The numbers -4 and -5 work perfectly because they multiply to 20 and add to -9.

Write the factored form

We put our two numbers into binomials. Each binomial is x minus one of our numbers.

Check by expanding the answer

✓

We multiply the binomials back together using FOIL to make sure we get our original expression. It matches, so our factoring is correct.

Understanding this problem

Learning Insight

Factoring a quadratic means finding two binomials that multiply together to create it. The key is that the two numbers in your binomials must multiply to give the last term (c) and add to give the middle coefficient (b). When you factor, you're basically reversing the FOIL process.

Quick Tip

When the last number is positive, both factors have the same sign. That sign matches the sign of the middle term. So if it's , both numbers are negative. If it were , both would be positive.

Common Mistake

Students often forget to make both numbers negative when the middle term is negative but the last term is positive. They might write instead of . Always check that your factors multiply AND add correctly to match the signs in the original problem.