 Factoring by Common Factor Factorise the polynomial: 3x 3 y 5 + 9x 2 y 6 - 12x y 7 Determine the GCF of the terms  GCF of 3, 9, and 12 is 3  The smallest.

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Factoring by Common Factor Factorise the polynomial: 3x 3 y 5 + 9x 2 y 6 - 12x y 7 Determine the GCF of the terms  GCF of 3, 9, and 12 is 3  The smallest power of x is 1.  The smallest power of y is 5  So the GCF is 3x y 5. GCF  Greatest Common Factor

Factoring by Common Factor Factorise the polynomial: 3x 3 y 5 + 9x 2 y 6 - 12x y 7 The GCF = 3x y 5 Factor out the GCF from each term:  3x 3 y 5 = 3x y 5 (x 2 ), 9x 2 y 6 = 3x y 5 (3x y) 12x y 7 = 3x y 5 (4y 2 ), So: 3x 3 y 5 + 9x 2 y 6 - 12x y 7 = 3x y 5 (x 2 + 3x y – 4y 2 ), GCF  Greatest Common Factor

The Grouping Method To factor by grouping: 1. Group terms so each group has a common factor. 2. Factor out the GCF of each group. 3. If the resulting terms have a common factor, factor that out. If not, you can try a different grouping GCF  Greatest Common Factor

The Grouping Method Factor by grouping: 6x 3 + 4x 2 – 3x – 2 Group: (6x 3 – 3x) + (4x 2 – 2) Factor out the GCF of each group: 3x (2x 2 – 1) + 2(2x 2 – 1) GCF  Greatest Common Factor

The Grouping Method 3x (2x 2 – 1) + 2(2x 2 – 1) Factor out the GCF of the two terms: (2x 2 – 1)(3x + 2) Check you result by multiplying: (2x 2 – 1)(3x + 2) = 6x 3 + 4x 2 – 3x – 2 GCF  Greatest Common Factor

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