In Exercises 34–37, solve each polynomial equation.34. 3x? = 5x + 235. (5x + 4)(x – 1) = 236. 15x? – 5x = 037. x - 4x2 - x + 4 = 0

34. Given polynomial function is: 3x2=5x+2 Rearranging the terms we get, 3x2-5x-2=0 Solving we get,…

Answered: In Exercises 34–37, solve each…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.3: Quadratic Equations

Problem 12E

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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 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 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 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 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"
5 (x+14)=85
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.
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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 37-46, use factoring to solve each polynomial equation. Check by substitution or by using a graphing utility and identifying x-intercepts. 37. x + 4x2 – 25x – 100 = 0 - 38. x - 2x2 – x + 2 = 0 39. x - x? = 25x – 25 40. x + 2x? 41. 3x* - 16х + 32 48x = 0 42. 5x4 – 20x? = 0 43. x* - 4x3 + 4x² = 0 44. x* – 6x + 9x? = 0 45. 2x + 16r² + 30x = 0 46. 3x3 – 9x2 30x = 0

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In Exercises 34–37, solve each polynomial equation. 34. 3x? = 5x + 2 35. (5x + 4)(x – 1) = 2 36. 15x? – 5x = 0 37. x - 4x2 - x + 4 = 0