8-2 Multiplying and Factoring

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8-2 Multiplying and Factoring Hubarth Algebra

Ex 1 Multiplying a Monomial Simplify –2g2(3g3 + 6g – 5) = –2g2(3g3) –2g2(6g) –2g2(–5) Use the Distributive Property. = –6g5 – 12g3 + 10g2 Simplify.

Ex 2 Finding the Common Factor Find the common factor of 2x4 + 10x2 – 6x. List the prime factors of each term. Identify the factors common to all terms. 2x4 = 2 • x • x • x • x 10x2 = 2 • 5 • x • x 6x = 2 • 3 • x The common factor is 2 • x, or 2x.

Ex 3 Factoring Out a Monomial Factor 4x3 – 8x2 + 12x. Step 1: Find the common factor. Step 2: Factor out the common factor. 4x3 = 2 • 2 • x • x • x 8x2 = 2 • 2 • 2 • x • x 12x = 2 • 2 • 3 • x 4x3 – 8x2 + 12x = 4x(x2) + 4x(–2x) + 4x(3) = 4x(x2 – 2x + 3) The common factor is 2 • 2 • x, or 4x.

Practice Simplify each product. a. 4𝑏(5 𝑏 2 +𝑏+6) b. -7h(3 ℎ 2 −8ℎ−1) c. 2x( 𝑥 3 +4 𝑥 2 −8𝑥+6) 2. Find the common factor of terms of each polynomial. 5𝑣 5 +10 𝑣 3 b. 4𝑏 3 −2 𝑏 2 −6𝑏 3. Use a common factor to factor each polynomial. a. 8𝑥 2 −12𝑥 b. 5𝑑 3 +10𝑑 c. 6𝑚 3 −12 𝑚 2 −24𝑚 20 𝑏 3 +4 𝑏 2 +24𝑏 −21 ℎ 3 +56 ℎ 2 +7ℎ 2 𝑥 4 +8 𝑥 3 −16 𝑥 2 +12𝑥 5𝑣 3 2b 4x(2x – 3) 5d( 𝑑 2 +2) 6𝑚( 𝑚 2 −2𝑚−4)