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DESCRIBING POLYNOMIALS:
Polynomial: A polynomial is one term or the sum or difference of two or more terms.
A polynomial has no variables in a denominator. For a term that has one variable, the degree of a term is the exponent of the variable.
x3 – 4x + 5x2 + 7 The degree of a
constant is 0.
degree 3 1 2 0
The degree of a polynomial is the same as the degree of the term with the highest degree. You can name a polynomial by its degree or by the number of its terms.
The polynomials in the chart are in standard form, which means the terms decrease in degree from left to right and no terms have the same degree.
Polynomial
Degree Name Using Degree
Number of Terms
Name Using Number of
Terms
7x + 4 1 Linear 2 Binomial
3x2 + 2x + 1
2 Quadratic 3 Trinomial
4x3 3 Cubic 1 Monomial
5 0 Constant 1 Monomial
EXAMPLE 1
Write each polynomial in standard form. Then name each polynomial by its degree and the number of its terms.
a. 5 – 2x b. 3x4 – 4 + 2x c. -2x + 5 – 4x2 + x3
EXAMPLE 2
Find (2x2 – 3x + 4) + (3x2 + 2x – 3)
EXAMPLE 3
Find (7x3 – 3x + 1) – (x3 + 4x2 – 2)
MULTIPLYING BY A MONOMIAL
You can use the distributive property to multiply polynomials.
Example 1: Multiply 3x and (2x + 1)
EXAMPLE 2
Multiply.a. 2x(4x – 3) b. (4x – 3)
(2x)
FACTORING OUT A MONOMIAL
Factoring a polynomial reverses the multiplication process. To factor out a monomial using the distributive property, it is helpful to find the greatest common factor (GCF).
Example 3: Find the GCF of the terms of the polynomial
4x3 + 12x2 – 8x
EXAMPLE 4
Find the GCF of the terms of each polynomial.
a. 4x3 – 2x2 – 6xb. 5x5 + 10x3
c. 3x2 – 18
EXAMPLE 5: FACTOR 3X3 – 9X2 + 15X
Step 1: Find the GCFStep 2: Factor out the GCF
EXAMPLE 6
Factor each polynomial.
a. 8x2 – 12xb. 5x3 + 10xc. 6x3 – 12x2 – 24x
HOMEWORK
Complete take home quiz.
