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Perfect Squares and Factoring

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.

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Perfect Squares and Factoring

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  1. Perfect Squares and Factoring

  2. 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

  3. 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

  4. 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? When factoring a perfect square trinomial, we can reverse this process by revising our 3 statements.

  5. 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

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

  7. 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.

  8. 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.

  9. 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

  10. 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

  11. 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.

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