Name: ______Date: ______

HW IM3 8.3.1Block: ____

8-92.Carlos is always playing games with his graphing calculator, but now his calculator has contracted a virus. The,, andfunctions on his calculator are not working. He needs to solvex3+5x2–16x–14 = 0, so he graphsy=x3+5x2–16x–14 and sees the graph below in the standard window.

  1. From the graph, what number appears to be an integer solution to the equation?
  2. Verify that your answer to part(a) is a solution.
  3. Since you know a solution to the equation, what is the factor associated with this solution?
  4. Use polynomial division to determine the other factor.
  1. Use your new factor to complete the following equation.

x3+ 5x2– 16x– 14 = 0
(x+7)(other factor)=0

  1. The “other factor” leads to two other solutions to the equation. What are the two other solutions? State all three solutions to the original equation.

8-93.Now Carlos needs to solve 2x3+ 3x2– 8x+ 3 = 0, but his calculator will still only create a graph with a standard viewing window. He sees that the graph of
y= 2x3+ 3x2– 8x+ 3 crosses thexaxis atx=1. What are all three solutions to 2x3+ 3x2– 8x+ 3 = 0?

8-94.Without actually multiplying, decide which of the following polynomials could be the product of (x– 2)(x+ 3)(x– 5). Justify your choice.

a. x3– 4x2– 11x– 5

b. 2x3– 4x2– 11x+ 30

c. x3– 4x2– 11x+ 30

d. 2x3– 4x2– 11x– 5

8-95.Consider the equation 5x2– 7x– 6 = 0 as you complete the partsbelow.

a. What are the factors of 5x2– 7x– 6?

b. What are the solutions to the equation 5x2– 7x– 6 = 0?

c. Explain the relationship between the factors of the polynomial expression and the solutions to the related equation.

8-97.Eniki has a sequence of numbers given by the formulat(n) = 4(5)n.

  1. What are the first three terms of Eniki’s sequence?
  1. Toby thinks the number 312,500 is a term in Eniki’s sequence. Is he correct? Justify your answer by either giving the term number or explaining why it is not in the sequence.
  1. Elisa thinks the number 94,500 is a term in Eniki’s sequence. Is she correct? Explain.

8-98.What is the equation of the line passing through the point (–2,5) that is perpendicular to the liney=–5x+2?

8-99.Which of the following binomials could be a factor ofx3– 9x2+ 19x+ 5? Explain your reasoning.

  1. x– 2
  2. x– 5
  3. x+ 3
  4. x+ 2

8-100.Now dividex3– 9x2+ 19x+ 5 by the factor that you chose in the previous problem. If it is a factor, use it and the resulting factor to determine all the roots of the polynomial. If it is not a factor, reconsider your answer to the previous problem and try a different factor.

8-101.Divide each of the following polynomials,P(x), byD(x) to write the quotientQ(x) and then rewrite the polynomial in the formP(x)=D(x)·Q(x)+R, whereRis the remainder.

a. P(x) = 2x4–x2+ 3x+ 5
D(x) =x– 1

b. P(x) =x5– 2x3+ 1
D(x) =x– 3

How are the solutions to the equation related to the leading coefficient and constant term in the original polynomial?

8-104.Evaluate each expression without using acalculator.

a. log(10)b. log()c. log(0)d. 10(2/3)log(27)