Chapter 5 Quiz Review

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Part 1 (No Graphing Calculator) 1) Rewrite each polynomial in standard form, classify by degree (quadratic, cubic, quartic, quantic, etc.) and classify by the number of terms (binomial, trinomial, polynomial). Polynomial

Rewrite in Standard Form

Classify by Degree

Classify by # of terms

𝑦 = 5𝑥 3 − 𝑥 4 𝑦 = 𝑥2 + 7 − 𝑥 𝑦 = 𝑥 2 + 8 − 4𝑥 − 2𝑥 3 𝑦 = 10𝑥 + 𝑥 5 2) Determine the end behavior based on the degree and the leading coefficient. Degree

Leading Coefficient

End Behavior

𝑓(𝑥) = 𝑥 4 − 2𝑥 3 + 𝑥 2 𝑓(𝑥) = 5𝑥 3 + 7𝑥 2 − 𝑥 + 9 𝑓(𝑥) = 6𝑥 3 − 9𝑥 − 𝑥 𝑓(𝑥) = −11𝑥 4 − 6𝑥 2 + 𝑥 + 3 𝑓(𝑥) = 𝑥 2 (𝑥 − 1)3 (𝑥 + 2) 𝑓(𝑥) = (𝑥 + 3)(𝑥 + 1)3 (𝑥 + 4) 3) State each zero and its’ multiplicity. Determine whether the graph will bounce on, wiggle through, or cross through each zero (x-intercept). Zeros 𝑓(𝑥) = (𝑥 + 4)(𝑥 − 1)2

𝑓(𝑥) = 𝑥 2 (𝑥 − 3)5 (𝑥 + 2)4 (𝑥 − 10)

Multiplicity

B, W, or C?

4) Factor each polynomial. State the zeros, their multiplicities, and whether the graph will bounce, wiggle, or cross through each zero (x-intercept). a. 𝑓(𝑥) = 2𝑥 3 − 10𝑥 2 + 12𝑥

Factored Form

Zeros

Multiplicity

B, W, or C?

Zeros

Multiplicity

B, W, or C?

b. 𝑓(𝑥) = 𝑥 3 − 9𝑥

Factored Form

5) Suppose a polynomial has the zeros: 𝑥 = −2, 1, 4 a. Write the polynomial function in factored form.

b. Write the polynomial function in standard form. Show your work.

6) Use the function 𝑦 = (𝑥 − 4)(𝑥 + 1)(𝑥 − 2)(𝑥 − 1) to answer the following questions. a. What are the x-intercepts? State whether they will bounce, wiggle, or cross.

b. What is the y-intercept? (plug in x = 0) c. What is the end-behavior? d. Sketch a graph of the function.

7) Write an equation in factored form for each polynomial graph. Assume each tick mark on the x-axis represents 1 unit. a.

b.

f(x) =

f(x) =

8) Find the real and imaginary solutions of the equation by factoring. a. 𝑥 3 + 64 = 0

b. 𝑥 3 − 27 = 0

c. 𝑥 4 + 2𝑥 2 − 3 = 0

d. 𝑥 4 − 8𝑥 2 = −16