ALGEBRA I - SECTION 8-2 (Multiplying and Factoring)

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ALGEBRA I - SECTION 8-2 (Multiplying and Factoring) 6/1/2019 ALGEBRA I @ SECTION 8-2 : MULTIPLYING and FACTORING

Simplify by distributing. 1) 3(2x + 5) 4) 2x(5x + 6) ANSWER : 6x + 15 ANSWER : 10x2 + 12x 2) -5(4x – 3) 5) -y2(y + 6) ANSWER : -20x + 15 ANSWER : -y3 – 6y2 3) 9(4x2 – 7) 6) 8w3 (4w2 + w – 8) ANSWER : 36x2 - 63 ANSWER : 32w5 + 8w4 – 64w3

The Greatest Common Factor (GCF) is the largest common term that is a factor of all of the original terms. Find the GCF. (Hint : do a prime factorization of each term. The GCF is written using all common factors along with their smallest exponents.) 7) 36 and 42 8) 24, 60, and 72 ANSWER : 6 ANSWER : 12

9) 48ab2; 54a3bc 10) 60x3y4z5; 120x2y4z3 11) 21xy2; 25z To find the GCF of two or more monomials, first find the GCF of the “numbers”. For the variables, the GCF includes all variables the monomials have in common with their SMALLEST exponents. 9) 48ab2; 54a3bc ANSWER : 6ab 10) 60x3y4z5; 120x2y4z3 ANSWER : 60x2y4z3 11) 21xy2; 25z ANSWER : 1

Factor each polynomial. 12) 7x - 49 15) 12x2 – 3x ANSWER : 7(x – 7) ANSWER : 3x (4x – 1) 13) b2 – 14b 16) 80a4 + 60a3 – 50a2 + 10a ANSWER : b(b – 14) ANSWER : 10a(8a3 + 6a2 – 5a + 1) 14) 10x3 + 3x2 ANSWER : x2 (10x + 3)

One of the sons is also a father. Two Fathers and Two Sons Riddle. Two fathers and two sons sat down to eat eggs for breakfast. They ate exactly three eggs, each person had an egg. The riddle is for you to explain how. One of the sons is also a father.