EXAMPLE 5 Factor completely. a) n3 8 b) c3 64 c) 125r3 27s3 Solution a) Use Steps 1–3 to factor. Step 1: Identify a and b. n3 8 T T (n)3 (2)3 What do you cube to get n3? n So, a n and b 2. Step 2: Remember, a3 b3 (a b)(a2 ab b2). What do you cube to get 8? 2 Write the binomial factor, then write the trinomial. Square a. Product Square b. Same sign of a and b n3 8 (n 2)(n)2 (n)(2) (2)2 Opposite sign Step 3: Simplify: n3 8 (n 2)(n2 2n 4) b) Step 1: Identify a and b. c3 64 T T (c)3 (4)3 What do you cube to get c3? c So, a c and b 4. What do you cube to get 64? 4 Step 2: Write the binomial factor, then write the trinomial. Remember, a3 b3 (a b)(a2 ab b2). Square a. Product Square b. Same sign of a and b c3 64 (c 4)(c)2 (c)(4) (4)2 Opposite sign Step 3: Simplify: c3 64 (c 4)(c2 4c 16) c) 125r3 27s3 Step 1: Identify a and b. 125r3 27s3 T T (5r)3 (3s)3 What do you cube to get 125r3? 5r So, a 5r and b 3s. What do you cube to get 27s3? 3s Write out the example as you are reading it! 384 CHAPTER 7 Factoring Polynomials www.mhhe.com/messersmith
messersmith_power_intermediate_algebra_1e_ch4_7_10
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