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# Algebra 7 Point 6

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### Algebra 7 Point 6

1. 1. 7.6 Combined Types of Factoring<br />Objective: <br /><ul><li>To factor polynomials completely
2. 2. To factor polynomials by grouping terms</li></ul>Frameworks: 10.P.5<br />
3. 3. The polynomial 3x2 - 27<br />can be factored in 2 steps:<br />3x2 – 27 = 3(x2 – 9)<br /> = 3(x + 3)(x – 3)<br />When a polynomial is factored into irreducible polynomials that have no common factor, then it is factored completely.<br />
4. 4. Steps in factoring completely:<br />1. Look for the GCF<br />2. Look for special cases.<br />difference of two squares<br />perfect square trinomial<br />3. If a trinomial is not a perfect square, look for two different binomial factors.<br />8t4 – 32t3 + 40t <br /> = 8t(t3 - 4t + 5)<br />4x2 – 9y2 = (2x)2 – (3y)2<br />x2 + 8x + 16 = x2 + 8x + 42<br />= (x + 4)2<br />6x2 + 11x – 10 <br /> = (2x + 5)(3x – 2)<br />
5. 5. Factor 8y3 + 12x2 + 4x<br />
6. 6. Factor 6x3 + 14x2 + 8x<br />
7. 7. Factor 3x5 – 243x<br />
8. 8. Factor 2m2 – 20mn + 50n2<br />
9. 9. Factor 5x4y – 80x2y3<br />
10. 10. Factor 5x – 5y + ax - ay<br />
11. 11. Do p. 265 1-15<br />