Problems of the Day 2  x 24x2y

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Presentation transcript:

Problems of the Day 2  52 16 4 11x 24x2y Write the prime factorization of each number. 1. 50 2. -24 Find the GCF of each pair of numbers. 3. 16 and 32 4. 20 and 36 Find the GCF each pair of monomials. 5. 44x and 33x3 6. 24x2y and 48x3y2 2  52 -1  23  3 16 4 11x 24x2y

Problems of the Day 7.) 27a + 18a3 8.) 20x2y3 – 24xy2 Factor each polynomial. 7.) 27a + 18a3 8.) 20x2y3 – 24xy2 9a(3 + 2a2) 4xy2(5xy – 6) 9.) 28r3 – 14r2 + 7r 7r(4r2 – 2r + 1)

Factor by grouping Problems of the Day 10.) 9x2 – 3xy + 6x – 2y 11.) 6a2 – 6ab + 3a – 3b (6a2 – 6ab) + (3a – 3b) 6a(a - b) + 3(a – b) (6a + 3)(a – b) (9x2 – 3x) + (6x – 2y) 3x(3x – y) + 2(3x – y ) (3x + 2)(3x – y)

Solving Equations by Factoring Algebra 1 ~ Chapter 9.2 day 2 Solving Equations by Factoring

Zero Product Property Some equations can be solved by factoring. Consider the following products – 6(0) = 0 0(-3) = 0 4xyz(0) = 0 0(a + 1) = 0 Notice that in each case, at least one of the factors is zero. These examples illustrate the Zero Product Property – If the product of two factors is 0, then at least one of the factors must be 0.

CHECK! CHECK! Here are two examples of solving equations by factoring where the equations are already factored! a.) 3x(x – 2) = 0 b.) (x – 4)(2x + 7) = 0 3x = 0 or x – 2 = 0 x – 4 = 0 or 2x + 7 = 0 x = 0 or x = 2 x = 4 or x = -3.5 CHECK! CHECK!

Example 1 – Solve each equation in Factored Form 6m = 0 or m – 5 = 0 d – 7 = 0 or 3d + 4 = 0 m = 0 or m = 5 d = 7 or x = -4/3 a.) 6m(m – 5) = 0 b.) (d – 7)(3d + 4) = 0 CHECK! CHECK!

Here are two more examples where the equations are not factored yet Here are two more examples where the equations are not factored yet. Therefore we must factor the polynomial first! Remember, we can only use the Zero Product Property if the equation is = 0! a.) 5y2 + 15y = 0 b.) a2 = 8a 5y(y + 3) = 0 a2 – 8a = 0 a(a – 8) = 0 5y = 0 or y + 3 = 0 y = 0 or y = -3 a = 0 or a – 8 = 0 a = 8

Example 2 – Solve each equation by factoring c.) 3m2 + 5m = 0 d.) 9y2 – 18y = 0 e.) 10m2 = 20m

Assignment Study Guide 9-2 (Homework) Skills Practice 9-2 #’s 19-26. (In Class) Quiz on Sections 9-1 to 9-2 on Thursday, April 14th!!!!!