10.1 Adding and Subtrac1ng Polynomials
Polynomial in standard form-­‐ An expression in descending form (The exponent decreases)
2x2 + 3x3 -­‐ x + 4 is not in standard form
3x3 + 2x2 -­‐ x + 4 is in standard form.
Leading coefficient-­‐ the coefficient of the first term when an expression is in standard form.
Terms are separated by + or -­‐ . monomial-­‐ 1 term
binomial -­‐ 2 terms
trinomial-­‐ 3 terms
polynomial -­‐ 4 or more
Degree-­‐ highest exponent in an expression
constant -­‐ no exponent linear -­‐ exponent=1 quadra1c -­‐ exponent=2 cubic -­‐ exponent=3
quar1c -­‐ exponent=4
Classifying Polynomials:
POLYNOMIAL
DEGREE
a. 7
0
b.
1
c.
1
d.
2
e.
3
f.
4
Classified by
Degree
Classified by
# of Terms
Adding and Subtracting Polynomials
- line all the terms up according to their degree
- combine like terms like we have done before
Example (2x2 + x + 5) + (x + x2 +6)
2x2 + x + 5
+ x2 + x + 6
3x2 + 2x + 11
3 terms, trinomial
degree = 2, quadratic
leading coefficient = 3
Example 2 (x2 - 8) - (7x + 3x2) (Distribute the - )
x2
-8
2
-3x -7x
-2x2 - 7x -8
trinomial, quadratic, lc=-2
Find sums of the following:
1.
3.
4.
2.
Find the differences:
1.
3.
4.
5.
2.