Factoring - Perfect Square Trinomial A Perfect Square Trinomial is any trinomial that is the result of squaring a binomial. Binomial Squared Perfect Square Trinomial

Our goal now is to start with a perfect square trinomial and factor it into a binomial squared. Here are the patterns. Perfect Square Trinomial Factored Note the pattern for the signs:

Here is how to identify a perfect square trinomial: 1.Both first and last terms are perfect squares 2.The middle term is given by If these two conditions are met, then the expression is a perfect square trinomial. Note that there is always a positive sign on both of these terms.

Example 1 Factor: Determine if the trinomial is a perfect square trinomial. 1.Are both first and last terms perfect squares? 2.Is the middle term

Since the trinomial is a perfect square, factor it using the pattern: 1.First term a: 2.Last term b: 3.Sign same as the middle term 4.Squared

Example 2 Factor: Determine if the trinomial is a perfect square trinomial. 1.Are both first and last terms perfect squares? 2.Is the middle term

Since the trinomial is a perfect square, factor it using the pattern: 1.First term: 2.Last term 3.Sign same as the middle term 4.Squared

Example 3 Factor: Determine if the trinomial is a perfect square trinomial. 1.Are both first and last terms perfect squares? 2.Check the middle term:

Since the trinomial is a perfect square, factor it using the pattern: 1.First term: 2.Last term 3.Sign same as the middle term 4.Squared

Example 4 Factor: Determine if the trinomial is a perfect square trinomial. 1.Are both first and last terms perfect squares? 2.Check the middle term: No This is not a perfect square trinomial. If it can be factored, another method will have to be used.

Example 5 Factor: Determine if the trinomial is a perfect square trinomial. 1.Are both first and last terms perfect squares? This is not a perfect square trinomial. If it can be factored, another method will have to be used. No

Example 6 Factor: Determine if the trinomial is a perfect square trinomial. This is not a perfect square trinomial since the last term has a negative sign. Perfect square trinomials always have a positive sign for the last term.

Example 7 Factor: Determine if the trinomial is a perfect square trinomial. 1.Are both first and last terms perfect squares? 2.Check the middle term:

Since the trinomial is a perfect square, factor it using the pattern: 1.First term: 2.Last term 3.Sign same as the middle term 4.Squared