Factor.

8-6 Perfect Squares and Factoring Algebra 1 Glencoe McGraw-HillLinda Stamper

In the previous lesson you worked with the difference of two squares (sum and difference pattern). Today the focus is on perfect square trinomials (square of a binomial pattern).

For a trinomial to be factorable as a perfect square, three conditions must be satisfied. The first term must be a perfect square. The middle term must be twice the product of the square roots of the first and last terms. The last term must be a perfect square.

x +2 Remember the square of a binomial is a SQUARE ?

x +3

x +4

To find the product… Square first term. Multiply the terms and then double it. Square last term. Factoring is working backwards from multiplying! Think – What is the square of the first term and what is the square of the second term.

Can you factor out a greatest monomial factor? Square of a Binomial Pattern Which answer/s are not factored completely? Could you use the X-Factor method to factor these problems?

Factor.

Do you recognize this Square of a Binomial Pattern? Square first term. Multiply the terms and then double it. Note: middle term is negative! Square last term.

x –2x –2 The middle term is always negative?

Square of a Binomial Pattern Which answer/s are not factored completely?

Example 1 Check using FOIL! Determine whether each trinomial is a perfect square trinomial. If so, factor it. Example 2 Example 3 Example 4 Example 5 Example 6 Example 7 Example 8 Example 9

When solving equations involving repeated factors, it is only necessary to set one of the repeated factors equal to zero. Doubl e root!

Use factoring to solve the equation. Remember if it is a perfect square, it is only necessary to set one of the repeated factors equal to zero Example 10 Example 11 Example 12 Example 13 Example 14 Example 15

Example 10 Example 11

Example 12 Example 13

Example 14

HOW TO APPROACH FACTORING PROBLEMS When factoring it is important to approach the problem in the following order. Look at the problem carefully and ask yourself: 1. Can I pull out a greatest common factor? If you can, do it, but then look at what is left to check for opportunities to factor again. 2. Is this the DIFFERENCE of Two Squares? Remember that these never have a middle (x) term. If so, factor it into the ( + )( – ) pattern. 3. Is this a Perfect Square Trinomial? If so, it will factor into two parentheses that are exactly the same and can be written as a square.

Check by doing FOIL. Remember that factoring is working backwards from multiplying. Always look at what remains and check for opportunities to factor further. 4.If you examined the problem closely and answered the above questions each with a NO, then you must factor using the X figure. Use the X-Factor method if the leading coefficient does not equal 1. HOW TO APPROACH FACTORING PROBLEMS 5.If there are four or more terms look to factor by grouping. Group terms with common factors and then factor out the GCF from each grouping. Then use the distributive property a second time to factor a common binomial factor.

8-A12 Pages #12–30,57–60.