By Harley Flanders and Justin J. Price (Auth.)
Algebra and Trigonometry
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X + 1 x3 + 1 6. x/2 + \2xyz + 9xz 2 ' Compute: 9 y' 1 i 1 10. 1 3 x-1 1 4 x+ 1 * — 1 x 11 * 2x + 3 2x + 5 Π 3 * ι ^ ι x2 — 4 x + 2 x - 2 14. 3x x2-4 15. * + ^ 7 x 16. 1 x 1 xy 17 *+-V x + 2/ 18. i y2 x2+y2' ! 7 x + 3/ 12. 1 2x + 1 x (JC 1 — 2)is 1 xy1 Multiply and express in lowest terms: «■ mm \x+//\x yf » (^κ^) \x—y/\x y/ Compute the quotient: 27. ^ ± 1 / - ^ 28. ^±f/(iL±Z) 2 29. 4^I/4±J_ 30. (a + x + 4/x + 4 a3 + a a2 + \ Simplify: x + 2y\ xy / b)2/a2-b2 ab 46 1. BASIC ALGEBRA „ 35, (U2 V2\/U* V*\ t (xu — yv)2 + (xv + yu)2 x2 +y2 34.
When we write JC2 + 5x + 6 = (x + 2)(x + 3), 10. Factoring we are factoring the left-hand side. If a given polynomial has integer coefficients, we generally look for factors with integer coefficients. A familiar kind of factoring is removing a common polynomial factor. Examples: x4 (3x - _ 6χ3 _ Ίχ2 = χ 2( χ 2 1)(JC2 + 4) + 2(3* - _ 6 χ _ 7)? 1)(4JC + 5) + (Sx - l) 2 = (3JC - l)[(x2 + 4) + 2(4* + 5) + (3* - 1)] = ( 3 J C - l)(x2 + 11JC+ 13). Most factoring depends on recognizing certain polynomial products.
1 / - ^ 28. ^±f/(iL±Z) 2 29. 4^I/4±J_ 30. (a + x + 4/x + 4 a3 + a a2 + \ Simplify: x + 2y\ xy / b)2/a2-b2 ab 46 1. BASIC ALGEBRA „ 35, (U2 V2\/U* V*\ t (xu — yv)2 + (xv + yu)2 x2 +y2 34. 36. x2y2 — 1 ** + * - 6 t2 + 4^ + A 12. C O M M O N ERRORS IN ALGEBRA The basic rules of algebra discussed in this chapter are indispensable in this course and all other mathematics courses you will take. It is worth the effort to master them now so you will avoid silly mistakes in the future. Let us Hst some of the most common types of errors in algebra.