Transcript 10.1 Adding and Subtracting polynomials

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
degree
3
1
2
0
The degree of
a constant is 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.
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
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.
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 – 6x
b. 5x5 + 10x3
c. 3x2 – 18
EXAMPLE 5: FACTOR 3X3 – 9X2 + 15X
Step 1: Find the GCF
Step 2: Factor out the GCF
EXAMPLE 6
Factor each polynomial.
a. 8x2 – 12x
b. 5x3 + 10x
c. 6x3 – 12x2 – 24x
HOMEWORK
Complete take home quiz.