Perfect Squares and Factoring

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Presentation transcript:

Perfect Squares and Factoring

Perfect square trinomials are the squares of binomials… WATCH… Square of a Difference These are binomials Square of a Sum Remember the short cut? Square the first term. Square the last term. Middle term is twice the product of the first and last terms

Middle term is twice the product of the first and last terms Square of a Difference Remember the short cut? Square the first term. Square the last term. Middle term is twice the product of the first and last terms

When factoring a perfect square trinomial, we can reverse this process by revising our 3 statements. OLD STATEMENTS: Square the first term… Square the last term… Middle term is twice the product of the first and last terms. NEW QUESTIONS: Is the first term a perfect square? Is the last term a perfect square? Is the middle term twice the product of the square roots of the first and last term?

Like this.... Is the middle term twice the product of the first and last factors? Is the first term a perfect square? Is the last term a perfect square? Yes Yes IF you answer YES to each question, it is a perfect square trinomial. You can write your answer as either the sum or difference of two squares. Yes

First term a perfect square? Last term a perfect square? YES... of 3x YES... of 2 Middle term twice the product? 2(3x)(2) = 12x ... YES You answered YES to everything, now write your answer.

First term a perfect square? Last term a perfect square? YES... of 4x YES... of 3 Middle term twice the product? 2(4x)(3) = 24x... YES You answered YES to everything, now write your answer.

What about these? First term a perfect square? Can you do this one without the questions? YES... of 3x Last term a perfect square? Now would be a good time to remind you that perfect squares are ALWAYS Positive…. WHY? YES... of 4 Middle term twice the product? 2(3x)(4) = 24x ... YES You answered YES to everything, now write your answer.

Prime Remember your questions: Is the first term a perfect square? Is the last term a perfect square? Is the middle term twice the product of the first and last factors? If you answer NO to ANY of these questions, you must try another way of factoring. YES... of 4x YES... of 1 2(4x)(1) = 8x .... NO Press if You get NO Prime YES... of 5x NO Press if You get NO Press if DONE

Scratch paper..... Press After #6 What factors of 16x2 will ADD to give +32x 1x(16x) NO 2x(8x) NO 4x(4x) NO None of these will ADD to give me 32x What factors of 150x2 will SUBTRACT to give -5x 1x(150x) NO 2x(75x) NO 3x(50x) NO 5x(30x) NO 6x(25x) NO 10x(15x) YES +10x – 15x = -5x Press After #7

So what have we learned? If the answer to all 3 questions is YES, then we can use the short cut to factor. If even ONE answer is NO, then we must use an alternate method to try to factor. If it can’t be factored, the answer is PRIME.