polynomials add and subtract ch 9.1
TRANSCRIPT
1. Be able to determine the degree of a polynomial.
2. Be able to classify a polynomial.
3. Be able to write a polynomial in standard form.
4. Be able to add and subtract polynomials
Monomial: A number, a variable or the product of a number and one or more variables.
Polynomial: A monomial or a sum of monomials.
Binomial: A polynomial with exactly two terms.
Trinomial: A polynomial with exactly three terms.
Coefficient: A numerical factor in a term of an algebraic expression.
Degree of a monomial: The sum of the exponents of all of the variables in the monomial.
Degree of a polynomial in one variable: The largest exponent of that variable.
Standard form: When the terms of a polynomial are arranged from the largest exponent to the smallest exponent in decreasing order.
A polynomial is a monomial or the sum of monomials
24x 83 3 x 1425 2 xx Each monomial in a polynomial is a term of the
polynomial.
The number factor of a term is called the coefficient.
The coefficient of the first term in a polynomial is the lead coefficient.
A polynomial with two terms is called a binomial.
A polynomial with three terms is called a trinomial.
14 x
83 3 x
1425 2 xx
The degree of a polynomial in one variable is the largest exponent of that variable.
2 A constant has no variable. It is a 0 degree polynomial.
This is a 1st degree polynomial. 1st degree polynomials are linear.
This is a 2nd degree polynomial. 2nd degree polynomials are quadratic.
This is a 3rd degree polynomial. 3rd degree polynomials are cubic.
Classify the polynomials by degree and number of terms.
Polynomial
a.
b.
c.
d.
5
42 x
xx 23
14 23 xx
DegreeNumber of
Terms
Classify by number of
terms
Zero 1 Monomial
First 2 Binomial
Second 2 Binomial
Third 3 Trinomial
To rewrite a polynomial in standard form, rearrange the terms of the polynomial starting with the largest degree term and ending with the lowest degree term.
The leading coefficient, the coefficient of the first term in a polynomial written in standard form, should be positive.
745 24 xxx
x544x 2x 7
Write the polynomials in standard form.
243 5572 xxxx
32x4x 7x525x
)7552(1 234 xxxx
32x4x 7x525x
Remember: The lead coefficient should be positive in standard
form.
To do this, multiply the polynomial by –1 using the distributive
property.
Write the polynomials in standard form and identify the polynomial by degree and number of terms.
23 237 xx 1.
2. xx 231 2
23 237 xx
33x 22x 7
7231 23 xx
723 23 xx
This is a trinomial. The trinomial’s degree is 3.
xx 231 2
23x x2 1
This is a 2nd degree, or quadratic, trinomial.
Find the Sum
Add (x2 + x + 1) to (2x2 + 3x + 2)
You might decide to add like terms as the next slide demonstrates.
Add Like Terms
+ 2x2 + 3x + 2x2 + x + 1 = 3x2+ 4x+3
Or you could add the trinomials in a column
Just like adding like-terms
+ 2x2 + 3x + 2
x2 + x + 1
3x2 + 4x +3
Start with the trinomials in a column
+ 2x2 + 3x + 2
Combine the trinomials going down
Problem #2
Try one.(3x2+5x) + (4 -6x -2x2)
Make sure you put the polynomials in standard form and line them up by degree.
(3x2+5x) + (4 -6x -2x2)
3x2+5x-2x2 -6x + 4
+ 0 It might be helpful to use a zero as a placeholder.
x2 -x + 4
Find the difference
- (3x2 - 2x + 3)
x2 + 2x - 4
-2x2 + 4x - 7
Start with the trinomials in a column
- (3x2 - 2x + 3)
The negative sign outsideof the parentheses is reallya negative 1 that is multipliedby all the terms inside.
- 3x2 + 2x - 3)
Try One.
- (10x2 + 3x + 2)
12x2 +5x + 11
2x2 + 2x + 9
Reminder:Start with the trinomials in a column
- (10x2 + 3x + 2)
The negative sign outsideof the parentheses is reallya negative 1 that is multipliedby all the terms inside.
- 10x2 - 3x - 2
Special Thanks
to Public Television Station KLVX for the basic outline of the first 12 slides of this presentation