Unit 7- Polynomials

What do I look for when classifying the “degree” of a polynomial?

The HIGHEST/LARGEST exponent

Degree of 0- Number by itself- no variable

Constant (5)

Degree of 1

Linear (b)

Degree of 2

Quadratic (10m²)

Degree of 3

Cubic (4b³)

Degree of 4

Quartic (15s⁴)

Degree of 5+

5th degree, 6th degree….. (10b⁸)

1 Term

Monomial (x²)

2 terms

Binomial (x⁴+3)

3 terms

Trinomial (m⁵+m²+m)

4+ terms

Polynomial (v⁶+5v⁵+v³+v)

Product Rule: a^m*aⁿ

a^m*aⁿ=a^m+n (add exponents)

Power Rule: (a^m)ⁿ

(a^m)ⁿ⁼a^m*n (multiply exponents)

Zero Exponent Rule: a⁰

a⁰=1. Anything raised to the ZERO power is 1

Quotient Rule: a^m/aⁿ

a^m/aⁿ=a^m-n (subtract exponents)

Power of Quotient Rule: (a/b)^m

(a/b)^m=a^m/b^m (apply the exponent to the numerator and denominator)

Negative Exponent Rule: a^-1

a^-1= a/a¹. Flip the location of the exponent and turn it positive. 

Constant

A number by itself (-3)

Coefficient

The number in front of a variable (the “-5” in -5x)

Variable

A letter that stands for an unknown number (the “x” in -5x)

Area of a rectangle/square formual

Area= length * width

Area of a triangle formula

Area= (length width)/2 OR Area=1/2 *length *width