Polynomial Functions of Higher Degree with Modeling Worksheet

**Page 1**

1.

The dimensions of a piece of tin are 18ft and 14ft . From this piece of tin an open box with a volume of 180ft³ is to be made by cutting a square of the same size from each corner and folding up the edges. Find the polynomial equation to find the length $x$ of the side of the square piece that is to be removed.

a. | $x$³ - 32$x$² + 252$x$ - 180 = 0 | ||

b. | $x$³ - 16$x$² + 63$x$ - 45 = 0 | ||

c. | 2$x$³ - 32$x$² + 126$x$ - 45 = 0 | ||

d. | $x$² - 32$x$ + 72 = 0 |

Draw a diagram showing the square corners to be cut from the piece of tin.

[Analyse and understand the Problem.]

Volume of box = 180 ft

As

[Use Volume = Length × breadth × height.]

252

[Expand.]

[Simplify.]

Correct answer : (2)

2.

A unit cube is removed from a cube of side $n$ cm. If the volume of the remaing cube is 728 cm^{3}, then find the side of the cube.

a. | 81 | ||

b. | 9 | ||

c. | 8 | ||

d. | 10 |

[Write the volume of the cube.]

The volume after the removal of a unit cube =

[Write the volume of the remaining part in terms of

[The volume of the remaining part is 728 cm

(

[Factor.]

[

The side of the cube is 9 cm

Correct answer : (2)

3.

Which of the following is the at most number of local extrema of a polynomial function of degree 5?

a. | 5 | ||

b. | 10 | ||

c. | 25 | ||

d. | 4 |

So, the atmost number of local extrema of a polynomial function of degree 5 is 4.

Correct answer : (4)

4.

Choose the largest number of zeros that a polynomial of degree 12 can have.

a. | 144 | ||

b. | 24 | ||

c. | 12 | ||

d. | 11 |

So, the at most number of zeros of a polynomial function of degree 12 is 12.

Correct answer : (3)

5.

Find the solutions of ($x$ + 3)^{3} ($x$ + 4) ($x$ - 6) = 0.

a. | - 3, - 4, - 6 | ||

b. | - 3, - 4, 6 | ||

c. | - 3, 4, 6 | ||

d. | - 3, 4, - 6 |

So, the solutions of the equation are

Correct answer : (2)

6.

Write the at most number of local extrema of the polynomial function $f$ ($x$) = 5$x$^{3} - 28$x$^{2} + 96$x$ + 73.

a. | 6 | ||

b. | 7 | ||

c. | 3 | ||

d. | 2 |

The at most number of local extrema of the given polynomial function is

[A polynomial function of degree

Correct answer : (4)

7.

Find the atmost number of local extrema possessed by the polynomial $f$ ($x$) = - $x$^{5} + 6$x$^{4} + 36$x$^{3} - 4$x$^{2} - 90$x$ + 41.

a. | 5 | ||

b. | 1 | ||

c. | 4 | ||

d. | 3 |

The atmost number of local extrema possessed by the given polynomial function is

[A polynomial function of degree

Correct answer : (3)

8.

Find the zeros of the function $f$ ($x$) = 8$x$^{2} - 10$x$ + 3 algebraically.

a. | $\frac{1}{2}$ and $\frac{3}{4}$ | ||

b. | - $\frac{1}{2}$ and - $\frac{3}{4}$ | ||

c. | $\frac{1}{2}$ and - $\frac{3}{4}$ | ||

d. | - $\frac{1}{2}$ and $\frac{3}{4}$ |

[Solve the related equation

8

[Factor.]

(2

2

So, the zeros of

Correct answer : (1)

9.

Find the maximum number of zeros possible for the polynomial $f$ ($x$) = $x$^{3} - 30$x$^{2} + 93$x$ - 77.

a. | 2 | ||

b. | 1 | ||

c. | 3 | ||

d. | 4 |

The maximum number of zeros possessed by the given polynomial function is

[A polynomial function of degree

Correct answer : (3)

10.

Find the maximum number of zeroes possible for the polynomial $f$ ($x$) = $x$^{4} - 23$x$^{3} + 93$x$^{2} - 238$x$ + 90.

a. | 1 | ||

b. | 2 | ||

c. | 3 | ||

d. | 4 |

The maximum number of zeroes possessed by the given polynomial function is

[A polynomial function of degree

Correct answer : (4)