3. Polynomials

3.01 Review: Operations with polynomials

3.02 Synthetic and long division

Investigation: Roller coaster polynomials

3.03 Graphs and characteristics of polynomial functions

3.04 Solving polynomial equations

3.05 Remainder and factor theorems

3.06 Roots and zeros

3.07 The binomial theorem

3.08 Proofs and further applications of polynomial identities

3.09 Polynomial identities and complex numbers

United States of America UT

Math III

3.02 Synthetic and long division

Interactive practice questions

Which of the following is the correct simplification of $\frac{z+10}{10}$z+1010?

$\frac{z}{10}+1$z10+1

A

$z+1$z+1

B

$z$z

C

Easy

< 1min

Simplify the following expression, for $x\ne0$x≠0:

$\frac{9x^3+5x^5}{x}$9x3+5x5x

Easy

< 1min

Simplify $\frac{18x^3-12x^2+24}{3}$18x3−12x2+243.

Easy

< 1min

Simplify the following expression, for $x\ne0$x≠0:

$\frac{48x^4+12x^3-30x^2-42x}{6x}$48x4+12x3−30x2−42x6x

Easy

1min

Outcomes

III.A.APR.6

Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

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