Polynomial Identities

NC Math 3 EOC Review

Polynomial Functions

Polynomial Vocabulary

Graphs of Polynomials

This 4th degree polynomial has:

Two x-intercepts (-5 and 5)

One y-intercept (about y=1)

Three turning points* and

Down-down tail behavior

*Turning points are where the graph transitions from increasing to decreasing or vice versa.

Bringing it all together

(10/28) Unit 3: Zeros of Polynomial Functions

Chapter 3: Polynomial Functions

Section 1: Graphing

Section 2: Adding, Subtracting, Multiplying

(Tomorrow, Section 3: Polynomial Identities)

Multiple Choice

Which selection is the final answer?

• $$4x+3-31$$  

• $$4x-28$$  

• $$4x+3-\frac{31}{4x+3}$$  

• $$4x+3-\frac{31}{x+5}$$  

Multiple Choice

Given the polynomial $$f\left(x\right)=x^3-2x^2-23x+60$$ , what is the distance between the closest zeros?

• 3

• 8

• 1

• 4

Multiple Choice

Which expression is equivalent to $$\frac{x+3}{6x-3}\div\frac{x^2+2x-3}{2x-1}$$ ?

• $$3\left(x-1\right)$$

• $$\frac{x-1}{3}$$

• $$\frac{3}{x-1}$$

• $$\frac{1}{3\left(x-1\right)}$$

Multiple Choice

If $$h\left(x\right)=2x$$ and $$g\left(x\right)=3x^2+1$$ , what is $$h\left(g\left(x\right)\right)$$ ?

• $$6x^2+1$$

• $$6x^2+2$$

• $$12x^2+1$$

• $$12x^2+2$$

Multiple Choice

Which polynomial function has the following zeros: $$3\ and\ 4+i$$ ?

• $$f\left(x\right)=x^3-11x^2+41x-51$$

• $$f\left(x\right)=x^3-5x^2-7x+51$$

• $$f\left(x\right)=x^3+5x^2-7x-51$$

• $$f\left(x\right)=x^3+11x^2+41x+51$$

Multiple Choice

Solve for x: $$-\frac{1}{2}\left|2x+6\right|+2=0$$ .

• x = 5 or x = 1

• x = 5

• x = -5 or x = -1

• x = -1

Multiple Choice

When interest is compounded n times a year, the acculated amount (A) after t years is given by the formula $$A=P\left(1+\frac{r}{n}\right)^{nt}$$ where P is the intial principle and r is the annual rate of interest. Approximately how long will it take $2,000.00 to double at an annual interest rate of 5.25% compounded monthly?

• 13.98 years

• 13.71 years

• 13.23 years

• 13.08 years

Multiple Choice

What is the vertical asymptotes of the function $$f\left(x\right)=\frac{4x^2-100}{2x^2+x-16}$$ ?

• $$x=5,\ x=-5$$

• $$x=-5,\ x=4,\ x=5$$

• $$x=-3,\ x=\frac{5}{2}$$

• $$x=-3,\ x=\frac{5}{2},\ x=\frac{20}{3}$$

Multiple Choice

Which is a solution set to the equation $$x+2=\frac{4}{x-2}$$ ?

• $$\left\{\pm2\ \sqrt[]{2}\right\}$$

• $$\left\{\frac{1\ \pm\ \sqrt[]{17}}{2}\right\}$$

• $$\left\{\frac{-1\pm\ \sqrt[]{17}}{2}\right\}$$

• $$\left\{\pm\ 2\right\}$$

Multiple Choice

Simplify: $$\frac{9x^4-25}{6x^2+10}$$ .

• $$\frac{3x^2-5}{2}$$

• $$3x^2-5$$

• $$\frac{3x^4-5}{2}$$

• $$x\left(3x^2-5\right)$$

​What is a Quadrant?

Each of the 4 quarters of a circle

• Quadrants of a circle are numbered

  going counter clockwise​

• The quadrant determines whether

  the x and y values are positive

  or negative​

Radians vs Degrees

Radian Conversion

You can use thei proportion to solve for either degrees(D) or radians(R). plug in your know value (R or D) and solve for the other

Converting Hints

• If you convert from Degrees, pi will show up in your answer for radians....

• Leave Pi as a symbol in radians! (unless you need a decimal answer)

• If you converting from Radians, pi will cancel out

ARC LENGTH

Multiple Choice

If the length of the 45° region of this circle is $$10\Pi$$   inches, what is the radius of the circle?

• 40 in.

• $$4\sqrt{5}$$  in.

• 10 in.

• 20 in.

7.4: Arc Length & Area of a Sector

Objective: Use proportional reasoning to find arc length and area of a sector

Arc Length

Ex 1: Find the length of the minor arc

Ex 2:

Area of a Circle & Semicircle

Area of a Quarter-Circle

Area of a Sector

Multiple Choice

Circle B includes arc XY that measures 4 feet. What is the length of Circle B's diameter, rounded to the nearest tenth.

• 7.8 ft.

• 48 ft.

• 7.6 ft.

• 15.3 ft.

Multiple Choice

Find the area of the shaded region.

• $$50.27\ in^2$$

• $$12.57\ in^2$$

• $$62.83\ in^2$$

• $$113.10\ in^2$$

Multiple Choice

Evaluate $$2f\left(1\right)+3f\left(4\right)$$ .

• 7

• 2

• 23

• 21

Multiple Choice

Which is the inverse of $$f\left(x\right)=1.5^x+4$$ ?

• $$f^{-1}\left(x\right)=\frac{x-4}{1.5}$$

• $$f^{-1}\left(x\right)=\frac{\log\left(x\right)-4}{1.5}$$

• $$f^{-1}\left(x\right)=\frac{\log\left(x-4\right)}{\log\left(1.5\right)}$$

• $$f^{-1}\left(x\right)=\frac{4-\log\left(x\right)}{\log\left(1.5\right)}$$

Multiple Choice

Martha can paint a room in 2 hours. Jamie can paint the same room in 6 hours. How long, to the nearest tenth of an hour, will it take them to paint the room together?

• 1.5 hours

• 3 hours

• 4 hours

• 2.5 hours

Multiple Choice

A company makes and boxes spaghetti.

~One machine fills each box with approximately 32 ounces of spaghetti.

~After the boxes are filled, another machine weighs each box.

~A box is discarded if the weight of the box differs by more than 0.25 ounce from the target weight of 32 ounces.

Which inequality can be used to find the range of acceptable weights, x, of the spaghetti?

• $$\left|x-0.25\right|\le32$$

• $$\left|x+0.25\right|\le32$$

• $$\left|x-32\right|\le0.25$$

• $$\left|x+32\right|\le0.25$$

Multiple Choice

A polynomial, $$p\left(x\right)$$ , has lead coefficient 1 and exactly 3 distinct zeros.
~  $$x=-1$$ is a zero of multiplicity two
~  $$x=2$$ is a zero of multiplicity one
~  $$x=4$$ is a zero of multiplicity one
What choice shows  $$p\left(x\right)$$  ? 

• $$p\left(x\right)=x^3-5x^2+2x+8$$  

• $$p\left(x\right)=x^3-5x^2+2x-8$$  

• $$p\left(x\right)=x^4-4x^3-3x^2+10x+8$$  

• $$p\left(x\right)=x^4+4x^3-3x^2-10x+8$$  

Multiple Choice

The graph of a function is shown below. Which interval is the graph negative?

• $$\left(-4,-1\right)$$

• $$\left[-2,0\right)$$

• $$\left(0,2\right]$$

• $$\left(0,4\right]$$

Multiple Choice

Given AB is a diameter of circle p and if m∠APC = 100°, find m∠CPB

• 50°

• 260°

• 130°

• 80°

Multiple Choice

What is the value of x?

• 18
• 8
• 10
• 30

Multiple Choice

What is the length of TR?

• 4
• 6
• 9
• 11