Simplify the following…
2(4 + x)
x(x – 3x
2
+ 2)
5x – 2 + 6x
2x
2
+ 5x – 11x
2
+ 1
8x(4x
2
)
Adding, Subtracting and Multiplying
Polynomials
Polynomial – A monomial or sum of
monomials.
Monomial – A number, variable, or product of
a number and 1 or more variables.
5x
Binomial – The sum of two monomials.
2x
2
+ 7
Trinomial – The sum of three monomials.
x
3
– 10x + 4
Degree of a Polynomial – The
greatest degree
of any term
in the polynomial.
Degree 0 = Constant
Degree 1 = Linear
Degree 2 = Quadratic
Degree 3 = Cubic
Example: 5x
3
+ 6x
2
– 2 Degree is 3 (Cubic)
Expression
Is
it a
Polynomial?
What is the
degree?
Monomial, Binomial,
or
Trinomial?
4x – 5yz
-6.5
7a
-3
+ 9b
6x
3
+ 4x + x + 3
Write the terms in order from greatest to
least degree.
4x
3
– 5x
2
+ 2x – 7
Your Turn… Write these in standard form.
1.
3x
2
+ 4x
5
– 8x
2.
x + 5x
3
– 2x
2
– 7x
6
+ 10
Method 1: Combine Like Terms!!!
(2x
2
+ 5x – 7) + (3 – 4x
2
+ 6x)
Method 2: Align and Combine!!!
(3x + x
3
– 5) + (4x
2
– 4x + 2x
3
+ 8)
Method: Distribute the negative. Then, solve
by adding.
(3 – 2x + 2x
2
) – (4x – 5 + 3x
2
)
(7x + 4x
3
– 8) – (3x
2
+ 2 – 9x)
-3x
2
(7x
2
– x + 4)
2x(-4x
2
+ 5x) – 5(2x
2
+ 20)
2x(5x – 2) + 3x(2x + 6) + 8 = x(4x + 1) + 2x(6x – 4) + 50
x(x + 3) – x(x – 4) = 9x – 16
8.1
8.2