Chapter 4 Review (College Algebra)

Chapter 4 Review

College Algebra

Sections in Chapter 4

• 4.1 Polynomials with Degree > 2

• 4.2 Polynomial Division

• 4.3 Zeros of Polynomials

• 4.4 Complex/Rational Zeros of Polynomials

• 4.5 Rational Functions

• 4.6 Variation

Multiple Choice

Which equation could represent the polynomial shown?

• $$f\left(x\right)=-2x^2+x-7$$

• $$f\left(x\right)=-2x^5+x^4+3x^3+7x^2-x-7$$

• $$f\left(x\right)=7x^5+x^4+3x^3+7x^2-x-7$$

• $$f\left(x\right)=x^4+3x^3+7x^2-x-7$$

Multiple Choice

Match the the graph with its factored form equation:

• $$f\left(x\right)=x^2\left(x+2\right)\left(x-5\right)\left(x-1\right)$$

• $$f\left(x\right)=-x^3\left(x-2\right)\left(x+5\right)\left(x+1\right)^2$$

• $$f\left(x\right)=\left(x+2\right)\left(x-5\right)^2\left(x-1\right)$$

• $$f\left(x\right)=-x\left(x+2\right)\left(x-5\right)\left(x-1\right)$$

Fill in the Blank

What is the y-intercept of $$f\left(x\right)=-7x^8-10x^7+2x^6+19x^5-x^4+x^3+8x^2-x+3$$ ?

Multiple Choice

If dividing $$\frac{x^3-7x^2+x-9}{3x^2-1}$$ , which method may be used?

• Long division only

• Long division or Synthetic division

• Synthetic division only

• neither

Fill in the Blank

What is the remainder when dividing $$\left(4x^4-3x^2-1\right)\div\left(x-2\right)$$ ?

Multiple Choice

Given $$x=1,\ 2$$ are roots, find the remaining roots of $$f\left(x\right)=3x^4-5x^3-8x^2+14x-4$$ .

• $$x=-\frac{1}{3},7$$

• $$x=-5,\ \frac{1}{2}$$

• $$x=\frac{-2\pm\ \sqrt[]{10}}{3}$$

• $$x=\frac{4\pm\ \sqrt[]{5}}{3}$$

Multiple Choice

Write a function with real coefficients which contains the roots $$x=2,\ 1-i$$ .

• $$f\left(x\right)=x^3-4x^2+6x-4$$

• $$f\left(x\right)=x^3-1$$

• $$f\left(x\right)=x^3-2x^2+3x-6$$

• $$f\left(x\right)=x^3+4x^2+4x-32$$

Fill in the Blank

If the function $$f\left(x\right)=a\left(x+1\right)\left(x-3\right)\left(2x-1\right)$$ passes through (2, -27), what is the value of a?

Multiple Choice

According to the image, which root has a multiplicity of 3?

• x = 1/2

• x = 2

• x = 3

• none of these

Multiple Choice

Use Descartes' Rule of Signs to find the possible number of imaginary roots of:

$$f\left(x\right)=-3x^6-4x^5+x^4-9x^3+10x^2-x+6$$

• 0 or 2 or 4

• 2 or 4

• 0 or 2

• 0

Multiple Choice

Which of the following could NOT be a possible rational root of:

$$f\left(x\right)=4x^3+x^2-9x+3$$

• x = 1

• x = -3/4

• x = 4

• x = -3

• x = 3/2

Multiple Choice

Select the TRUE statement about $$f\left(x\right)=\frac{4x^2-9x+2}{2x^2-x-6}$$

• No horizontal asymptote, 2 vertical asymptotes, 1 oblique asymptote, no hole

• 1 horizontal asymptote, 2 vertical asymptotes, no oblique asymptote, no hole

• 1 horizontal asymptote, 1 vertical asymptote, no oblique asymptote, 1 hole

• 1 horizontal asymptote, 1 vertical asymptote, 1 oblique asymptote, 1 hole

Multiple Choice

Match the image with its function.

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

• $$f\left(x\right)=\frac{2\left(x+1\right)\left(x-4\right)}{\left(x-1\right)\left(x-5\right)}$$

• $$f\left(x\right)=\frac{\left(x-1\right)\left(x-4\right)}{\left(x+1\right)\left(x-5\right)}$$

• $$f\left(x\right)=\frac{2\left(x+1\right)\left(x+4\right)}{\left(x-1\right)\left(x+5\right)}$$

Fill in the Blank

Given y is directly proportional to x, but inversely proportional to z, find the constant of variation between the three, when x = 9, z = 3, and y = 27.

That's it!

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• Non-circled homework exercises are good too!

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