Transcript Lesson 10.1 Add and Subtract Polynomials

Warm Up
Given f(x)= 3x-x and g(x)=5x+2
Evaluate
f (2)  4
a) f(2)
g (3  x)  5 x  17
b) g(3-x)
f (4)  g (8)  50
c) f(4)+g(8)
f (3)  g (1)  42
d) f(3) * g(1)
g ( y  2)  5 y  12
e) g(y+2)
Use the graph to find the following:
f) f(1)
g) f(-2) + f(1)
h) f(X) = 0
f(1) = -8
f(-2) + f(1) = 2
f(x) = 0, x = -3, 0, 3
Monomial: A number or a product of numbers
and variables with whole number exponents. One
term.
Examples:
4
2
3
4
x , 4a b,12, x y z
Polynomial: A sum or difference of monomials.
Examples:
x  8x
2
x  8x  2x
3
2
3x 2  2 x
3x3  2 x 2  5 x

The degree of a polynomial with only one
variable is the largest exponent of that
variable.
12x2 - 7 + 4x3 + x7

The Degree is 7 (the largest exponent of x)
Degree of a Polynomial
x  8x
2
2z  9z
12
3t  t
2
3
3

The Standard Form for writing a polynomial is
to put the terms with the highest degree first.
(highest exponent to lowest exponent)
Example: Put this in Standard Form:
 3x2 - 7 + 4x3 + x6


The highest degree is 6, so that goes first, then
3, 2 and then the constant last:
x6 + 4x3 + 3x2 - 7
Are these polynomials in standard form?
2x  6x  2x  x
2
4
3
5 x  3x  8 x  17
3
2
Like Terms
Like terms are terms that contain the
same variables, with corresponding
variables having the same power.
Example :
3x2+4x+x2-2
The like terms in this expression are:
3x 2 and x 2
Group the like terms
1. 7x2+8x-2y+8-6x
2. 3x-2y+4x2-y
3. 6y+y2-3+2y2-4y3
(3x  7  x)  (14 x  2  x  x)
2
3

Line up with like terms

Add like terms

2
Write in standard form (descending order)
3
2
14 x  4 x  0 x  9
(2x2+3x-4) + (4x2+4x+8)

Line up with like terms

Add like terms

Write in standard form (descending order)

1.
(36 x  6 x  11)  (6 x  16 x  5)
2
2
3
16 x  30 x  6 x  16
3

2.
2
(5x  12  6 x )  (15x  3x  2)
3
2
2
5 x  9 x  3x  14
3
2
(1  x )  (3x  2 x  5)
2
2

Distribute the negative Sign

Add like terms

Write in standard form
Example: 2
(y2-8y+10) - (3y2+8y+10)
1.Distribute the negative Sign
2.Add like terms
3.Write in standard form
1. (3x2+3x+3) - (4x2-2x+1)
2. (3a3+7a-1) - (3a2+3a-4)


On a scale of 1-10 how do you feel about this lesson?
 1 being super easy I could do this in my sleep.
 10 being I’m not going to lie, I fell asleep and
have NO clue what is going on!!!!!!!
Homework: Work sheet 10.1