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Chapter 6.7 Factoring: A General Strategy

Chapter 6.7 Factoring: A General Strategy. Tanya Yang period 2. Factoring Polynomials: Step one. Always look for a common factor. Ex: 2x+2. Common factor is 2, so 2(x+1). Factoring polynomials: step Two.

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Chapter 6.7 Factoring: A General Strategy

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  1. Chapter 6.7 Factoring: A General Strategy Tanya Yang period 2.

  2. Factoring Polynomials: Step one • Always look for a common factor. Ex: 2x+2. Common factor is 2, so 2(x+1)

  3. Factoring polynomials: step Two • 2. Look at the number of terms. If there is two terms, determine if the two terms are a difference of squares. • ex: x2-16= (x+4)(x-4)

  4. Factoring polynomials: Step Two cont. • If there is three terms, determine if the trinomial is a square of a binomial. If not, use the X and the lattice boxes. • ex: 2x4+8x3+6x2 There is a greatest common factor of 2x2(GCF) • 2x2(x2+4x+3) This is not a square of a binomial, so we must use the X • So we must multiply the 3 with the x2 to get 3x2 to place on the top and use the middle term(4x) as the bottom. • To find the left and right terms, you must find two terms that multiply to 3x2 and add to 4x X 3x^2 x To input the numbers, put the first term, x2, in the top left, the 3x in the top right, the 1x in the bottom left, and the 3 in bottom right. 3x 4x x 3 Now, using the lattice box, input the numbers and find the GCF. x 1 Final answer is 2x2(x+1)(x+3)

  5. Factoring Polynomials: Step Two Cont. • If there is four terms, factor by grouping. Use the lattice box • Ex: 3x3+12x2-2x-8 Place the first term in the top left,the second term in the top right, the third term in the bottom left, and the last term in the bottom right. Then find the GCF. Don’t forget the subtraction signs! x 4 3x2 -2 Final answer is (x+4)(3x2-2)

  6. Factoring Polynomials: Step three • Always make sure to factor completely. Many questions have tricks in them, • ex: (x4-16) This is a difference of squares. • = (x2+4)(x2-4) There is still one more difference of squares. • = (x2+4)(x-2)(x+2)

  7. Resource(s) Used • Textbook pg. 283

  8. Thanks for Watching!

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