Name
Date
Class
Reteach
LESSON
6-1
Polynomials
The degree of a polynomial is the value of the exponent of the term of the greatest degree.
A polynomial is in standard form when the terms are arranged in order with exponents from
greatest to least.
Degree Polynomial in Standard Form
0
Constants have degree 0.
8
1
2x 3
2
x 4x 5
3
4x 3 x
4
6x 4 x 3 5x 2 3x 1
5
9x 5 x 3 1
This third degree polynomial
has 2 terms.
2
This fifth degree polynomial
has 3 terms.
To arrange the polynomial 3x 2 x 4 2x 6x 5 7 in standard form, order the terms from
greatest to least exponent.
6x 5 x 4 3x 2 2x 7
6 is the leading
coefficient of this
polynomial.
Rewrite each polynomial in standard form. Then identify the leading
coefficient, degree, and number of terms of each polynomial.
1. 2x x 3 x 2 5
2. 5x 2 3x 4 x
Standard form: x 3 x 2 2x 5
Standard form: 3x 4 Leading coefficient: 1
Leading coefficient:
Degree:
3
Degree:
4
Number of terms:
3
4. 3x 2 x 4 x 2x 3 8
7x 5 6x 3
Standard form:
Standard form:
7
Leading coefficient:
Degree:
3
4
Number of terms:
3. 6x 3 7x 5
5x 2 x
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a207c06-1_rt.indd 6
1
Leading coefficient:
5
Number of terms:
x 4 2x 3 3x 2
x8
Degree:
2
4
Number of terms:
6
5
Holt Algebra 2
12/29/05 8:31:24 PM
Process Black
Name
Date
Class
Reteach
LESSON
6-1
Polynomials (continued)
To add polynomials:
− Write each polynomial in standard form.
− Align like terms vertically.
− Add like terms.
Standard form: x 3 4x 2 2x
Add: 6x 2x 3 5x 2 1 4x 2 2x x 3 .
Standard form: 2x 3 5x 2 6x 1
2x 3 5x 2 6x 1
Align like terms.
x 4x 2x
3
2
Add like terms vertically.
3x 3 x 2 8x 1
To subtract polynomials, add the opposite vertically.
3
2
2
3
Subtract: 6x 2x 5x 1 4x 2x x .
3
2
2
3
Add the opposite: 6x 2x 5x 1 4x 2x x .
3
2
2x 5x 6x 1
3
2
x 4x 2x Add like terms vertically.
x 3 9x 2 4x 1
Write each polynomial in standard form. Add or subtract.
2
3
2
5. 3x 2x x 6x 2x 1 6. x 4x 3 5 4x 2 x 2x 3 4x 3
x5
3
2
2x 4x x
2x 3 3x 2 x
2x 2 6x 1
2x 3 5x 2 5x 1
6x 3 4x 2 5
7. 6x 2 4x 1 2x x 3 1 8. 4x 3 6 3x 2 x 3 Add the opposite:
Add the opposite:
6x 2 4x 1 2x x 3 1 6x 2 4x 1
x3
2x 1
x 3 6x 2 2x 2
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a207c06-1_rt.indd 7
(4x 3 6) (3x 2 x 3)
4x 3
6
3
2
x 3x
5x 3 3x 2 6
7
Holt Algebra 2
5/15/06 1:56:19 PM
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