Examples for

# Common Core Math: High School Algebra: Polynomials & Rational Expressions

A monomial is the product of a number (called a coefficient) and variables raised to nonnegative integer powers (e.g. 4x^{2}). A polynomial is a mathematical expression that can be written as the sum of one or more monomials (e.g. 4x^{2} + 5x^{3}). In high school, students learn to compose polynomials via addition, subtraction and multiplication and to decompose polynomials via factoring and division. A rational expression is a ratio of two polynomials. Students extend their knowledge of polynomials to manipulate and perform arithmetic with rational expressions. In the course of their studies of polynomial arithmetic, students learn and apply two key theorems: the binomial theorem and the remainder theorem.

### Common Core Standards

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### Factor Polynomials

Decompose and analyze polynomials in terms of their factors.

#### Factor polynomials (CCSS.Math.Content.HSA-APR.C.4):

#### Find zeros of a polynomial (CCSS.Math.Content.HSA-APR.B.3):

#### Recognize and apply polynomial identities (CCSS.Math.Content.HSA-APR.C.4):

#### Apply the remainder theorem (CCSS.Math.Content.HSA-APR.B.2):

### Add, Subtract & Multiply Polynomials

Combine polynomials via addition, subtraction or multiplication.

#### Identify polynomials (CCSS.Math.Content.HSA-APR.A.1):

#### Add and subtract polynomials (CCSS.Math.Content.HSA-APR.A.1):

#### Multiply polynomials (CCSS.Math.Content.HSA-APR.A.1):

#### Apply the binomial theorem (CCSS.Math.Content.HSA-APR.C.5):

### Rational Expressions

Rewrite and compute with ratios of polynomials.