Download Adding/Subtracting Polynomials (1/4/17)

8.1Adding and Subtracting Polynomials
monomial – number, variable or the product of numbers and
variables
polynomial – monomial or the sum or difference of
monomials
standard form of a polynomial – written with terms in
order from greatest to least (highest to lowest power)
leading coefficient – the coefficient of the first term
Ex: Write each polynomial in standard form, then
give the leading coefficient.
Leading
Polynomial
Standard Form
Coefficient
3
2
3
2
1. 20x – 4x + 2 – x
-4x – x + 20x + 2
-4
3
5
5
3
2. y + y + 4y
y + y + 4y
1
To add and subtract polynomials, combine like terms.
Adding Polynomials
Ex: 15m3 + 6m2 + 2m3
17m3 + 6m2
3x2 + 5 – 7x2 + 12
-4x2 + 17
.9y5 - .4y5 + .5x5 + y5
.5x5 + 1.5y5
2x2y – x2y – x2y
0
Ex: (2x2 – x) + (x2 + 3x – 1)
2x2 – x + x2 + 3x – 1
3x2 + 2x – 1
(-2ab + b ) + (2ab + a)
-2ab + b + 2ab + a
a+b
(4b5 + 8b) + (3b5 + 6b – 7b5 + b)
4b5 + 8b + 3b5 + 6b – 7b5 + b
15b
Subtracting Polynomials
(2x2 + 6) – (4x2)
2x2 + 6 – 4x2
-2x2 + 6
(a4 – 2a) – (3a4 – 3a + 1)
a4 – 2a – 3a4 + 3a - 1
-2a4 + a – 1
(3x2 – 2x + 8) – (x2 – 4)
3x2 – 2x + 8 – x2 + 4
2x2 – 2x + 12
(11z3 – 2z) – (z3 – 5)
11z3 – 2z – z3 + 5
10z3 – 2z + 5