Quiz 2

Mth 163 Test-Unit II Name___________________________

Sections 4.2-4.5, 2.5

1. Identify the left-hand and right-hand behavior of the graph of the polynomial

function f(x) = 6x 3 – 5x + 4.

2. Find a polynomial function that has zeros at -3, -1, and -2. Do not leave it in

factored form, but multiply out your answer.

3. Use the Intermediate Value Theorem to determine an interval bounded by integers

one unit in length in which the polynomial function is guaranteed to have a zero.

[EXPLAIN]

f(x) = 3x 5 – 9x

4 + 5x

3 – 4x

2 + x – 3

4. Use synthetic division to determine which of the following is a solution of the

equation 3x 4 – 2x

3 + 26x

2 – 18x – 9 = 0.

[A] 3 [B] 1 [C] - 3 [D] 1/3 [E] None of these

5. Use synthetic division to divide 4x 4 – 4x

3 -8x – 14 by x – 2. Show your work and

state the quotient and remainder.

6. Factor 2x 3 + 15x

2 + 27x +10 given that x+2 is one of the factors. SHOW YOUR

WORK.

7. Determine the maximum number of zeros of the polynomial function

f(x) = 7x 2 + 7x – 7x +2.

8. Use the Rational Zero Theorem to determine all possible rational zeros of

f(x) = 3x 5 – 6x

3 – 2x

2 + 9

Do not find the actual zeros.

9. Find all the real zeros of the function f(x) = x 3 + 2x

2 – 13x + 10. SHOW YOUR

WORK.

10. A polynomial function of degree 5 whose coefficients are real numbers has the

zeros 2, -9i, and -9+i. Identify the remaining zeros.

11. Write this polynomial in completely factored form: 10x 3 +29x

2 + 4x – 15. SHOW

YOUR WORK.

12. Use the Remainder Theorem, not direct substitution, to find f(-2) when

f(x) = 4x 3 + 3x + 10. Show your work and specify what f(-2) is.

13. Wouldn’t it be nice to win a million dollars? Most people think so, but one thing

many forget to consider is the amount of taxes that must be paid on the winnings. The

table below shows the relationship between the winnings and the approximate amount

of taxes to be paid to the IRS. Draw a scatter plot to model the data. Then find an

equation for the best-fit line and use the equation to estimate the amount of taxes to

be paid on winnings of $5,300,000.

Amount Won Taxes Due

$470,000 $100,000

$670,000 $180,000

$1,420,000 $480,000

$1,995,000 $710,000

2,545,000 $930,000