Unit 1: Polynomials

Perform arithmetic operations on polynomials, extending beyond the quadratic polynomials

(Standard A.APR.1).

Understand the relationship between zeros and factors of polynomials

(Standards A.APR.2–3).

Use polynomial identities to solve problems

(Standards A.APR.4–5).

Rewrite rational expressions

(Standards A.APR.6–7).

Section 1: Adding & Subtracting Polynomials

1.1  What is a polynomial?

Introduction to Polynomials

Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer. For example, 3x+2x-5 is a polynomial. This video covers common terminology like terms, degree, standard form, monomial, binomial and trinomial.

1.2 Adding & Subtracting Polynomials

Adding Polynomials

Adding polynomials is the same as the procedure used in combining like terms. When adding polynomials, simply drop the parenthesis and combine like terms. 

Subtracting Polynomials

When subtracting polynomials, distribute the negative first, then combine like terms.

Section 2: Multiplying Polynomials

2.1  Multiplying a monomial by a polynomial

Heading 1 text goes here

Use distributive property and the product rule of exponents to multiply a monomial by a polynomial.

Multiplying a monomial by a polynomial example

2.2 Multiplying binomials with leading coefficients of 1

Question:

Multiply. 

(v - 7)(v + 1)

Simplify your answer


Explanation:

We want to remove the parentheses from the product (v - 7)(v + 1).

We first multiply each term in the first factor (v - 7) by each term in the second factor (v + 1) using FOIL (First, Outer, Inner, Last).

F:  Multiply the first two terms:  v*v = v^2

O:  Multiply the two outside terms:  v*1 = v

I:  Multiply the two inside terms:  -7*v = -7v

L:  Multiply the last two terms:  -7*1 = -7

The product (v - 7)(v + 1) is then equal to the sum of these terms.

(v - 7)(v + 1) = v^2 + v - 7v - 7 = v^2 - 6v - 7