A monomial is a number, a variable or a product of a number and a variable where all

exponents are whole numbers. That means that

42, 5x, 14x12, 2pq

all are examples of monomials whereas

4 + y, 5 14*, 2pq'2

are not since these numbers don't fulfill all criteria.

The degree of the monomial is the sum of the exponents of all included variables.

Constants have the monomial degree of 0.

If we look at our previous examples we can see that

Monomial Degree

42 0

5x 0 + 1 = 1

14X12 0 + 12=12

2pq 0+1+1=2

A polynomial as oppose to the monomial is a sum of monomials where each monomial

is called a term. The degree of the polynomial is the greatest degree of its terms. A

polynomial is usually written with the term with the highest exponent of the variable

first and then decreasing from left to right. The first term of a polynomial is called the

leading coefficient.

4x5 + 2xz - lAx + 12

Polynomial just means that we've got a sum of many monomials. If we have a

polynomial consisting of only two terms we could instead call it a binomial and a

polynomial consisting of three terms can also be called a trinomial.

Example

What's the degree of the following polynomials?

X2 + X

The first monomial has a degree of 2 and the second monomial has a degree of 1.

The highest degree is 2 which mean that the degree of the polynomial is 2.

4, 2 and 1 , the highest degree is 4 which mean that the degree of the polynomial is 4.

X4 + X2 + X

We can add and subtract polynomials. We just add or subtract the like terms to

combine the two polynomials into one.

Example:

Add the polynomials. (4X + 8) + (3X + 2)

We take away the parentheses and group all like terms. 4x+ 8 + 3x + 2

4x + 3x + 2 + 8

We add all like terms to get the sum of the polynomials.

7x + 10

Example:

Subtract the polynomials.

We remove the parentheses and since we got a negative sign before the

second parenthesis we need to change the signs.

Now we subtract all like terms to find the difference between the two polynomials.

(4x ♦ 8) - (3x + 2)

4x + 8 - 3x - 2

4x - 3x - 2 + 8

x + 6

Video lesson: Add the two polynomials

(x2 + 3x + 8) + (3x2 - 2x + 4)

To see the solution look at the video in the next page.

Here we have an algebraic expression and we want to simplify it as much as possible. It’s two polynomials that we’re going to add together. The first polynomial is (x2 + 3x + 8). We’re going to add that to the polynomial (3x2 - 2x + 4). We can see that both of these polynomials are quadratics because the highest order is two. So to add these we simply add the like terms. So we have x squared terms, we have cross terms or just x terms and we have number terms. So we can add each of those like terms together and then we’ll have three terms in our final answer. So x squared plus 3x squared gives us 4x squared. 3x + -2x or 3x – 2x gives us just a single x value. Finally 8 + 4 gives us twelve. So these two polynomials add together to give us this new polynomial

With the subtracting the polynomials, why does it end up with x+6 as the answer when it's a subtraction example?