68 CHAPTER R Review of Basic Concepts 12x-2 - 8x-3 = 4x-313x-2-1-32 - 2x-3-1-322 Factor. = 4x-313x - 22 Simplify the exponents. CHECK 4x-313x - 22 = 12x-2 - 8x-3 ✓ Multiply. (b) 4m1/2 + 3m3/2 = m1/214 + 3m2 The least exponent is 1/2. Factor out m1/2. (c) 1y - 22-1/3 + 1y - 222/3 = 1y - 22-1/331 + 1y - 224 Factor out 1y - 22-1/3. = 1y - 22-1/31y - 12 Simplify. S Now Try Exercises 115, 119, and 125. R.6 Exercises CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. 1. The process of finding polynomials whose product equals a given polynomial is called . 2. A polynomial is factored completely when it is written as a product of . 3. Factoring is the opposite of . 4. When a polynomial has more than three terms, it can sometimes be factored using . 5. There is no factoring pattern for a in the real number system. In particular, x2 + y2 does not factor as 1x + y22, for real numbers x and y. CONCEPT PREVIEW Work each problem. 6. Match each polynomial in Column I with its factored form in Column II. I (a) x2 + 10xy + 25y2 (b) x2 - 10xy + 25y2 (c) x2 - 25y2 (d) 25y2 - x2 II A. 1x + 5y21x - 5y2 B. 1x + 5y22 C. 1x - 5y22 D. 15y + x215y - x2 7. Match each polynomial in Column I with its factored form in Column II. I (a) 8x3 - 27 (b) 8x3 + 27 (c) 27 - 8x3 II A. 13 - 2x219 + 6x + 4x22 B. 12x - 3214x2 + 6x + 92 C. 12x + 3214x2 - 6x + 92 8. Which of the following is the correct factorization of 6x2 + x - 12? A. 13x + 4212x + 32 B. 13x - 4212x - 32 C. 13x + 4212x - 32 D. 13x - 4212x + 32 9. Which of the following is the correct complete factorization of x4 - 1? A. 1x2 - 121x2 + 12 B. 1x2 + 121x + 121x - 12 C. 1x2 - 122 D. 1x - 1221x + 122 LOOKING AHEAD TO CALCULUS The technique of Example 8(c) is used often in calculus.
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