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
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Q: In Exercises 41-43, divide using long division. 41. (4x – 3x - 2x + 1) + (x + 1) 42. (10x – 26x? +…
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Q: In Exercises 34–37, solve each polynomial equation. 34. 3x? = 5x + 2 35. (5x + 4)(x – 1) = 2 36.…
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Q: Exercises 108–110 will help you prepare for the material covered in the next section. 108. Multiply:…
A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…
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A:
Q: In Exercises 105–107, factor each polynomial. Assume that all variable exponents represent whole…
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Q: Exercises 110-112 will help you prepare for the material covered in the next section. 110. Evaluate…
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A: Let's find.
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Q: 11. Write the polynomial in standard form. 5x – 2+ 4x + 8x?
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Q: In Exercises 35-44, factor the greatest common binomial factor from each polynomial. 35. 4(х + 3) +…
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Q: In Exercises 132–137, factor each polynomial. Assume that all variable exponents represent whole…
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Q: write a polynomial in standard form that has the given zeros: 1,-2+√7, -2-√7
A: Given problem:- write a polynomial in standard form that has the given zeros: 1,-2+√7, -2-√7
Q: In Exercises 35-36, divide the polynomial by the топоmial. 35. (15.x3 – 30x2 + 10x – 2) ÷ (5.x2) 36.…
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Q: Exercises 151–153 will help you prepare for the material covered in the next section. 151. Replace…
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Q: Exercises 141–143 will help you prepare for the material covered in the next section. In each…
A: Since you have asked multiple question, we will solve the first question for you. If you want any…
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- 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 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 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 106–108, factor and simplify each algebraic expression. 106. 16x + 32r4 107. (x² – 4)(x² + 3) - (r? – 4)°(x² + 3)2 108. 12x+ 6xIn 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 = 0In 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)
- 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 -In Exercises 105–107, factor each polynomial. Assume that all variable exponents represent whole numbers. 105. x4n + xn + x3n 106. 3x3" ym – 6x2my2m 107. 8y2n+4 + 16y2n+3 12y2"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 115–116, express each polynomial in standard form-that is, in descending powers of x. a. Write a polynomial that represents the area of the large rectangle. b. Write a polynomial that represents the area of the small, unshaded rectangle. c. Write a polynomial that represents the area of the shaded blue region. 115. -x + 9- -x +5- x + 3 x + 15 -x + 4- x + 2 116. x + 3 x + 1In 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 – 70xFor 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)