SECTION A.3 Polynomials A25 Squares of Binomials, or Perfect Squares x a x ax a 2 2 2 2 ( ) + = + + (3a) x a x ax a 2 2 2 2 ( ) − = − + (3b) Cubes of Binomials, or Perfect Cubes ( ) + = + + + x a x ax a x a 3 3 3 3 2 2 3 (4a) ( ) − = − + − x a x ax a x a 3 3 3 3 2 2 3 (4b) Difference of Two Cubes x a x ax a x a 2 2 3 3 ( ) ( ) − + + = − (5) Sum of Two Cubes x a x ax a x a 2 2 3 3 ( ) ( ) + − + = + (6) Now Work problems 49, 53, and 57 4 Divide Polynomials Using Long Division The procedure for dividing two polynomials is similar to the procedure for dividing two integers. In the division problem detailed in Example 5, the number 15 is called the divisor , the number 842 is called the dividend , the number 56 is called the quotient , and the number 2 is called the remainder . To check the answer obtained in a division problem, multiply the quotient by the divisor and add the remainder. The answer should be the dividend. For example, we can check the results obtained in Example 5 as follows: 56 15 2 840 2 842 ⋅ + = + = Dividing Two Integers Divide 842 by 15. Solution EXAMPLE 5 ) 15 842 75 92 90 2 56 So, 842 15 56 2 15 . = + Divisor → ← Quotient ← Dividend ← ⋅ 5 15 ← Subtract and bring down the 2. ← ⋅ 6 15 ← Subtract; the remainder is 2. Quotient Divisor Remainder Dividend ⋅ + =
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