Special Cases in Factoring Polynomials

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Presentation transcript:

Special Cases in Factoring Polynomials Chapter 10.5

Factoring Quadratic Binomials 49x2 – 25 The difference between two squares. The two binomial factors will be the same except for the sign between terms. The factors will be created by the square-root of each part. The square-root of 25 is 5. 49x2 – 25 The square-root of 49x2 is 7x. = (7x + 5)(7x – 5)

Perfect Square Trinomials x2 – 12x + 36 The last term will be a perfect square. The middle term will be twice the square-root of the last term. The sign of both binomials is the same as the sign in front of the middle term. = (x – 6)(x – 6) = (x – 6)2

If you can, always factor out the GCF 18x2 – 200 GCF of 18x2 – 200 2 divides evenly into 18 and –200. 2(9x2 – 100) The remaining binomial is a difference of squares. 2(3x – 10)(3x + 10) Remember, they will have different signs.

In your notebooks, factor the following: 1) x2 – 16x + 64 2) x2 + 16x + 64 3) x2 – 64 = (x – 8)2 = (x + 8)2 = (x – 8)(x + 8)

Homework: pg 489 (5-20 all)