Download Adding and Subtracting Polynomials

Adding and
Subtracting
Polynomials
Module VII, Lesson 1
Algebra Online
VHS@PWCS
What is a polynomial?
A polynomial is one term or the sum or
difference of two or more terms.
Examples of polynomials are:
5xy
2
3x  3x  9
2
12a 14
We classify polynomials by degrees or by
number of terms.
Classifying by Degree
Degree of a term is the exponent of the
term.
x4 + 2x2 – 4
The degreeThe degree
The degree
The degree
a polynomial
is the degree
of thisofterm
is
of 2x2 isof2 any
4. with the constant
for the term
highest ispower. In
0.
this case it is 4.
Classifying by Degrees
Polynomials with degrees of 0 – 3 have
special names. They are:
 0 degree – constant
 1st degree – linear
 2nd degree – quadratic
 3rd degree - cubic
Classifying By Number of
Terms
Polynomials can also be named by the number of
terms that make it up.
One term (6xy)
Monomial
Two terms (4x – 9)
Binomial
Three terms (5d2 + 5d – 10)
Trinomial
Three or more terms is considered a polynomial
Classify each polynomial by it’s
degree and number of terms.
1. 2x2
1. Quadratic monomial
2. 4b3 – 3b + 8
2. Cubic trinomial
3.
-2t4
4. 5
+ 5t
3. 4th degree binomial
4. 0 degree constant
Simplifying Polynomials
Recall from earlier lessons that to add or subtract
terms they must have exactly the same variable.
5x2 + 12x2 = 17x2
2w3 – 4w + 3w3 = 5w3 – 4w
-3r3 + 5r3 – 8r3 = -6r3
14x – 9 = 14x - 9
Just add or subtract
the coefficients of
terms with the same
variable
Adding Polynomials
(5x2 – 3x + 7) + (2x2 + 5x - 7)
To add these polynomials we just add the like terms. The
easiest way to do this is like we always have added. Line
them up on top of each other and add.
5 x 2  3x  7
2 x 2  5 x  7
7x2 + 2x
Subtracting Polynomials
(2x3 + 4x2 – 6) – (3x3 + 2x – 2)
Recall that subtracting is the same as adding the
opposite. So change everything in the second
polynomial to its opposite and add.
2x  4x  0x  6
3
2
  3x3  0 x 2  2 x  2
-x3 + 4x2 – 2x - 4
Try some on your own.
1. (3y2 + 5y – 6) + (7y2 – 9)
1. 10y2 + 5y – 15
2. (9y – 7x + 15a) + (-3y + 8x – 8a)
2. 6y + x + 7a
3. (7a – 10b) – (3a + 4b)
3. 4a – 14b
4. (5x2 – 4) – (3x2 + 8x + 4)
4. 2x2 – 8x - 8
Wrap-Up
 Polynomials can be classified by degree
(constant, linear, quadratic or cubic) or
number of terms (monomial, binomial
and trinomial).
 Terms can only be added or subtracted if
they have the exact same variable.