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Algebra 7 Point 6

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