|
In this lesson we will be
extending the concept of dividing a monomial by a monomial to dividing a
polynomial by a monomial.
First let's review the vocabulary.
 Monomial |
A
monomial is an algebraic expression which contains just one term.
That term could be a variable, a number, or a number attached to a
variable.
Here are some examples of monomials:
x, a, dc, 5, -4, 3x, -7xy |
|
Polynomial |
A
polynomial
is an algebraic expression which contains more than one
term.
In a polynomial the terms must be connected by
either a "+" or a
"-"
sign.
Here are some examples of polynomials:
8a+9y (2 terms called a binomial)
3x+5v-7 (3 terms called a trinomial)
12a2-4a+7x-6y
(more than 3 terms is just called a polynomial) |
Ok...now that we have reviewed the vocabulary let's
learn how to divide a polynomial by a monomial.
Example:
|
Divide (4x4 + 6x3 - 10x2) ÷ (2x)
It might look more difficult than it actually is....
You see...all we need to do is to divide (2x) into each of the terms,
one at a time....
(4x4 + 6x3 - 10x2) ÷ (2x)
Step 1: divide 4x4 by 2x
4x4 ÷ 2x = 2x3
Step 2: divide 6x3 by 2x
6x3 ÷ 2x = 3x2
Step 3: divide -10x2 by 2x
-10x2 ÷ 2x = -5x
After doing each of the separate divisions we put each of the
individual answers together....make sure to connect them with the
correct sign.
So...the final answer is:
2x3 + 3x2 - 5x |
Let's try another....
Let's try to do this one all in one step....
just be careful to watch the signs
and remember to subtract the exponents when you divide!
|
(25a5 + 15a4 - 35a3
- 40a2 + 10a) ÷ (5a)
Solution:
5a4 + 3a3 - 7a2 -
8a + 2 |
I think you've
got it!
Click here for some more practice
|
