Answered: In Exercises 112–114, multiply or… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.4: Fractional Expressions

Problem 70E

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In Exercises 112–114, multiply or divide as indicated.
x* + 6x + 9 x + 3
112.
3x + x
6x + 2
113.
x2 - 4 x - 2
x2 - 1
X - 1
x? - 5x - 24
x2 - 10x + 16
114.
x? - x - 12
x? + x - 6

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In Exercises 106–108, factor and simplify each algebraic expression. 106. 16x + 32r4 107. (x² – 4)(x² + 3) - (r? – 4)°(x² + 3)2 108. 12x+ 6x
In Exercises 129–132, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 129. 9x? + 15x + 25 = (3x + 5) 130. x - 27 = (x – 3)(x² + 6x + 9) 131. x³ – 64 = (x – 4)3 132. 4x2 – 121 = (2x – 11)
In Exercises 132–137, factor each polynomial. Assume that all variable exponents represent whole numbers. 132. 9x2" + x" – 8 133. 4x2n – 9x" + 5 134. an+2 – a"+2 – 6a? 135. b2n+2 + 3b"+2 10b2 136. 3c"+2 10c"+1 + 3c" 137. 2d"+2 5d"+1 + 3d"
In Exercises 133–136, factor each polynomial completely. Assume that any variable exponents represent whole numbers. 133. y + x + x + y 134. 36x2" – y2n 135. x* 3n 12n 136. 4x2" + 20x"y" + 25y2m
In Exercises 126–129, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 126. Once a GCF is factored from 6y – 19y + 10y“, the remaining trinomial factor is prime. 127. One factor of 8y² – 51y + 18 is 8y – 3. 128. We can immediately tell that 6x? – 11xy – 10y? is prime because 11 is a prime number and the polynomial contains two variables. 129. A factor of 12x2 – 19xy + 5y² is 4x – y.
In Exercises 83–90, perform the indicated operation or operations. 83. (3x + 4y)? - (3x – 4y) 84. (5x + 2y) - (5x – 2y) 85. (5x – 7)(3x – 2) – (4x – 5)(6x – 1) 86. (3x + 5)(2x - 9) - (7x – 2)(x – 1) 87. (2x + 5)(2r - 5)(4x? + 25) 88. (3x + 4)(3x – 4)(9x² + 16) (2x – 7)5 89. (2x – 7) (5x – 3)6 90. (5x – 3)4
For Exercises 115–120, factor the expressions over the set of complex numbers. For assistance, consider these examples. • In Section R.3 we saw that some expressions factor over the set of integers. For example: x - 4 = (x + 2)(x – 2). • Some expressions factor over the set of irrational numbers. For example: - 5 = (x + V5)(x – V5). To factor an expression such as x + 4, we need to factor over the set of complex numbers. For example, verify that x + 4 = (x + 2i)(x – 2i). 115. а. х - 9 116. а. х? - 100 117. а. х - 64 b. x + 9 b. + 100 b. x + 64 118. а. х — 25 119. а. х— 3 120. а. х — 11 b. x + 25 b. x + 3 b. x + 11
For Exercises 8–10, a. Simplify the expression. Do not rationalize the denominator. b. Find the values of x for which the expression equals zero. c. Find the values of x for which the denominator is zero. 4x(4x – 5) – 2x² (4) 8. -6x(6x + 1) – (–3x²)(6) (6x + 1)2 9. (4x – 5)? - 10. V4 – x² - -() 2)
Exercises 141–143 will help you prepare for the material covered in the next section. In each exercise, factor the polynomial. (You'll soon be learning techniques that will shorten the factoring process.) 141. x? + 14x + 49 142. x? – 8x + 16 143. х2 — 25 (or x? + 0х — 25)
Make Sense? In Exercises 135–138, determine whether each statement makes sense or does not make sense, and explain your reasoning. 135. Knowing the difference between factors and terms is important: In (3x?y)“, I can distribute the exponent 2 on each factor, but in (3x² + y)', I cannot do the same thing on each term. 136. I used the FOIL method to find the product of x + 5 and x + 2x + 1. 137. Instead of using the formula for the square of a binomial sum, I prefer to write the binomial sum twice and then apply the FOIL method. 138. Special-product formulas have patterns that make their multiplications quicker than using the FOIL method.
In Exercises 30–33, factor the greatest common factor from each polynomial. 30. 16x3 + 24x² 31. 2x 36x2 32. 21x?y – 14xy² + 7xy 33. 18r'y? – 27x²y
Exercises 143–145 will help you prepare for the material covered in the next section. In each exercise, factor completely. 143. 2r + 8x? + 8x 144. 5x3 – 40x?y + 35xy2 145. 96?x + 9b²y – 16x – 16y -

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