Question

Please help! Will give Medal.
Polynomials and Polynomial Functions Unit Test lesson 11 unit 5

Answer 1

1.

Which equation is most likely represented by the graph above?

(1 point)y = (2x – 1)(2x – 3)(2x + 5)
y = (2x + 1)(2x + 3)(2x – 5)
y = –(2x + 1)(2x + 3)(2x – 5)
y = (2x + 1)(2x + 3)(2x + 5)

2. The graph of is shown below.



What are the apparent zeros of the function graphed above?

(1 point){–1, 2.5}
{–17, 5}
{–4, 0, 2}
{–2, 0, 4}

3. What is a polynomial function in standard form with zeros 1, 2, –2, and –3? (1 point)x4 + 2x3 + 7x2 – 8x + 12
x4 + 2x3 – 7x2 – 8x + 12
x4 + 2x3 – 7x2 + 8x + 12
x4 + 2x3 + 7x2 + 8x + 12

Multiple Choice
4. What are the zeros of the function? What are their multiplicities?

f(x) = 5x3 – 5x2 – 30x (1 point)The numbers 3, –2, and 0 are zeros of multiplicity 1.
The numbers 3, –2, and 0 are zeros of multiplicity 2.
The numbers –3, 2, and 0 are zeros of multiplicity 1.
The numbers –3, 2, and 0 are zeros of multiplicity 2.

5. What are the real or imaginary solutions of the polynomial equation?
x3 – 8 =0 (1 point)1 + isquare root 3, and 1 – isquare root 3
2, –1 + isquare root 3, and –1 – isquare root 3
2, 1 + 2isquare root 3, and 1 – 2i square root 3
2, 2 +2isquare root 3, and 2 – 2isquare root 3

6. Which is equivalent to the following expression?

(3m2 + 2mn – n2) + (m2 + 4mn – n2) (1 point)4m2 + 6mn – 2n2
4m4 – 6mn – 2n4
3m2 – 6mn + 2n2
4m2 + 6mn + 2n2

7. Which is a factored form of 27x3 + 64? (1 point)(3x + 4)(9x2 – 24x + 16)
(3x + 4)(9x2 + 24x + 16)
(3x + 4)(9x2 – 12x + 16)
(3x + 4)(9x2 + 12x + 16)

Multiple Choice
8. Divide –2x3 – 4x2 + 3x + 2 by x – 3. (1 point)–2x2 – 10x – 27, R –79
–2x2 – 10x –27
–2x2 – 10x – 27, R 83
–2x2 – 10x + 27, R 83

9. Find the roots of the polynomial equation.

x3 – x2 + x + 39 (1 point)1 + 3i, 1 – 3i, –3
1 + 3i, 1 – 3i, 3
–2 + 3i, –2 – 3i, –3
2 + 3i, 2 – 3i, –3

10. Which correctly describes the roots of the following cubic equation?

x3 + 6x2 + 11x + 6 (1 point)One real root, two complex roots
Two real roots and one complex root
Three real roots, two of which are equal in value
Three real roots, each with a different value

11. What is the second term of (p + q)5? (1 point)25p4
5p4q
25p4q
125p4q

12. One zero of f(x) = x3 + 2x2 – 5x – 6 is 2. What are other zeros of the function? (1 point)1 and 3
–1 and –3
2 and –3
2 and 3

13. Which of the following quartic functions has x = –2 and x = –3 as its only two real zeros? (1 point)x4 – 5x3 + 7x2 – 5x + 6
x4 + 5x3 + 7x2 + 5x + 6
x4 + 5x3 + 7x2 – 5x – 6

x4 – 5x3 + 7x2 + 5x – 6

14. Work Pad

Note: Remember to show all of the steps that you use to solve the problem. You can use the comments field to explain your work. Your teacher will review each step of your responses to questions 13–19 to ensure you receive proper credit for your answers.

The design of a digital box camera maximizes the volume while keeping the sum of the dimensions at 6 inches. If the length must be 1.5 times the height, what should each dimension be?

Hint: Let x represent one of the dimensions, and then define the other dimensions in terms of x. (2 points)

15. What are the real or imaginary solutions of the polynomial equation?

x4 – 41x2 = –400 (2 points)

16. Use synthetic division to find P(–3) for P(x) = x4 – 2x3 – 4x + 4. (2 points)

17. Find all the zeroes of the equation.

x4 – 6x2 – 7x – 6 = 0 (2 points)

18. Use Pascal’s triangle to expand the binomial.

(d – 5y)6 (2 points)

19. What is the equation of y = x3 with the given transformations?
vertical compression by a factor of 1 over 7, horizontal shift 8 units to the left, reflection across the x-axis (2 points)

20. What are all the real zeroes of y = (x –12)3 – 7? (2 points)