# Schaum's Outline of Precalculus (3rd Edition) (Schaum's by Fred Safier

By Fred Safier

Tricky try out Questions? neglected Lectures? no longer adequate Time?

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738 absolutely solved problems
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Additional resources for Schaum's Outline of Precalculus (3rd Edition) (Schaum's Outlines Series)

Sample text

FACTORING. If the polynomial ax2 ϩ bx ϩ c has linear factors with rational coefficients, write it in factored form, then apply the zero-factor property that AB ϭ 0 only if A ϭ 0 or B ϭ 0. 2. SQUARE ROOT PROPERTY. If the equation is in the form A2 ϭ b, where b is a constant, then its solutions are found as A ϭ 2b and A ϭ Ϫ 2b, generally written A ϭ Ϯ 2b. 3. COMPLETING THE SQUARE. a. Write the equation in the form x2 ϩ px ϭ q. b. Add p2/4 to both sides to form x2 ϩ px ϩ p2/4 ϭ q ϩ p2/4. c. The left side is now a perfect square.

A rational expression is one which can be written as the quotient of two polynomials. Every polynomial P can be written as P/1, where numerator and denominator are polynomials; hence every polynomial is also a rational expression. 3. Perform indicated operations: x2 Ϫ 4y2 Ϭ (x2 Ϫ 3xy ϩ 2y2) xy ϩ 2y2 3 4x Ϫ 2 2 (d) ϩ Ϫ 2 xϪ1 xϩ1 x Ϫ1 x2 Ϫ 7x ϩ 12 # x3 Ϫ 6x2 ϩ 9x x2 Ϫ 9 x3 Ϫ 4x2 1 1 (c) Ϫ x xϩh (a) (b) (a) Factor all numerators and denominators, then reduce by removing any common factors. (x Ϫ 3)(x Ϫ 4) x(x Ϫ 3)2 (x Ϫ 3)2 x2 Ϫ 7x ϩ 12 # x3 Ϫ 6x2 ϩ 9x # ϭ ϭ 2 3 2 2 (x Ϫ 3)(x ϩ 3) x (x Ϫ 4) x(x ϩ 3) x Ϫ9 x Ϫ 4x (b) Change division to multiplication, then proceed as in (a).

Ans. 39. A 6-gallon radiator is filled with a 40% solution of antifreeze in water. How much of the solution must be drained and replaced with pure antifreeze to obtain a 65% solution? Ans. 40. Machine A can complete a job in 8 hours, working alone. Working together with machine B, the job can be completed in 5 hours. How long would it take machine B, working alone, to complete the job? Ans. 41. Machine A can do a job, working alone, in 4 hours less than machine B. Working together, they can complete the job in 5 hours.