In Exercises 83–92, factor by introducing an appropriatesubstitution.83. 2r* – x? – 384. 5x4 + 2x2385. 2r6 + 11x³ + 1586. 2x + 13x3 + 1587. 2y10 + 7y + 388. 5y10 + 29y – 4289. 5(x + 1)2 + 12(x + 1) + 7 (Let u = x + 1.)90. 3(x + 1) - 5(x + 1) + 2 (Let u = x + 1.)91. 2(x – 3) – 5(x – 3) – 792. 3(x – 2) – 5(x – 2) – 2

To factor the polynomial: 2x4-x2-3 Solution: 2x4-x2-3Substituting x2=t in above expression we…

Answered: In Exercises 83–92, factor by…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.5: The Binomial Theorem

Problem 13E

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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
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 106–108, factor and simplify each algebraic expression. 106. 16x + 32r4 107. (x² – 4)(x² + 3) - (r? – 4)°(x² + 3)2 108. 12x+ 6x
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 -
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)
In Exercises 117–120, factor out the greatest common factor from each expression. 117. 6x2 + 2x2 118. 8x4 + 4x4 119. 15x - 60x 1 120. 7.x3 – 70x
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
In Exercises 117–120, factor out the greatest common factor from each expression. 117. 6x2 + 2x² 5 118. 8x4 + 4x4 119. 15.x3 60x 120. 7x - 70x
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 69–-80, factor completely. 69. x* - 5x?y? + 4y* 70. x* - 10x?y² + 9y 71. (x + y) + 6(x + y) + 9 72. (x – y)? – 8(x – y) + 16 73. (x - y)* – 4(x – y) 74. (x + y) – 100(x + y) 75. 2x2 - 7ху?+ 3у 7xy + 3y 76. 3x? + 5xy? + 2y 77. х3 — у — х +у 78. x + y3 + x? – y? 79. xy + x3 - 8x'y – 8 80. xy – x + x*y° - 1 6,3
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.

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