This document discusses factoring polynomials by finding the greatest common factor (GCF). It provides examples of factoring polynomials by taking out the GCF of 5y2 + 10y + 20, t5 + 8t4 + t3, and 2b4 - 10b3 + 8b2. It also discusses using the distributive property to factor polynomials like 3x2 - 9x + 6.

1. 7.2 Greatest Common Monomial FactorObjective: To factor out the greatest common monomial factor from a polynomialFrameworks: 10.P.3, 10.P.5

2. What is the area of this rectangle?xy5

3. What is the area of this rectangle?5x + 5y OR 5(x + y)xy5

4. FactoringThe distributive property can be used to multiply a polynomial by a monomial:2(x2 – 3x – 5) = 2x2 – 6x - 10The distributive property can also be used to factor polynomials:3x2 – 9x + 6 = 3(x2 – 3x + 2)

5. Factor out the GCF from 5y2 + 10y + 20Find the GCF:5y2 – 5*y210y = 5*2y20 = 5*4Write each term as a product of 5 and a monomial:5(y2) + 5(2y) +5*(4)Use the distributive property:5(y2 + 2y +4)

6. Factor out the GCF from t5 + 8t4 + t3

7. Factor out the GCF from 2b4 – 10b3 + 8b2

8. Factor out the GCF from 24a2b5 – 8a7b6 + 12a4b3

9. Find the area of the shaded region:Write the result in factored form.Area of square:Area of circle:r

10. Do p. 250 1-20

12. FOIL With Negatives(x - 3)(x - 5)First terms: x and x x2Outside terms: x and 5 -5xInside terms: 3 and x -3xLast terms: 3 and 5 15Answer: x2 + -8x + 15