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 OH

High School

3.01 Review: Operations with polynomials

Interactive practice questions

Is $2x^3-4x^5+3$2x3−4x5+3 a polynomial?

Yes, it is a polynomial.

A

No, it is not a polynomial.

B

Medium

< 1min

Is $3x^3+\frac{2}{x^7}-1$3x3+2x7−1 a polynomial?

Medium

< 1min

Is $\sqrt{2}x^6+7x$√2x6+7x a polynomial?

Medium

< 1min

For the polynomial $P\left(x\right)=2x^7+2x^5+2$P(x)=2x7+2x5+2

Medium

< 1min

Outcomes

A.SSE.1

Interpret expressions that represent a quantity in terms of its context.

A.SSE.1.a

Interpret parts of an expression, such as terms, factors, and coefficients.

A.SSE.1.b

Interpret complicated expressions by viewing one or more of their parts as a single entity.

A.SSE.2

Use the structure of an expression to identify ways to rewrite it. For example, to factor 3x(x − 5) + 2(x − 5), students should recognize that the "x − 5" is common to both expressions being added, so it simplifies to (3x + 2)(x − 5); or see x^4 − y^4 as (x2)^2 − (y2)^2, thus recognizing it as a difference of squares that can be factored as (x^2 − y^2)(x^2 + y^2).

A.APR.1b

Understand that polynomials form a system analogous to the integers, namely, that they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Extend to polynomial expressions beyond those expressions that simplify to forms that are linear or quadratic

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