Given f(x)= 3x-x and g(x)=5x+2Evaluatea) f(2)b) g(3-x)c) f(4)+g(8)d) f(3) * g(1)e) g(y+2)

Warm Up

(2) 4(3 ) 5 17(4) (8) 50(3) (1) 42( 2) 5 12

fg x xf gf gg y y

Use the graph to find the following:

f) f(1)g) f(-2) + f(1) h) f(X) = 0

f(1) = -8f(-2) + f(1) = 2f(x) = 0, x = -3, 0, 3

Monomial: A number or a product of numbersand variables with whole number exponents.

Oneterm.

Examples:

Polynomial: A sum or difference of monomials.

Examples:

4 2 3 4, 4 ,12,x a b x y z

2 8x x 23 2x x

3 28 2x x x 3 23 2 5x x 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)

2 8x x12 32 9z z

Degree of a Polynomial

2 33t t

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?

2 4 32 6 2x x x x 3 25 3 8 17x x x

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:

3x2 and x2

Like Terms

1. 7x2+8x-2y+8-6x

2. 3x-2y+4x2-y

3. 6y+y2-3+2y2-4y3

Group the like terms

Line up with like terms

Add like terms

Write in standard form (descending order)

2 3 2(3 7 ) (14 2 )x x x x x

234 9041 xx x

(2x2+3x-4) + (4x2+4x+8)

Line up with like terms

Add like terms

Write in standard form (descending order)

1.

2.

2 2 3( 36 6 11) (6 16 5)x x x x

3 2 2(5 12 6 ) (15 3 2)x x x x

3 216 30 6 16x x x

3 25 9 3 14x x x

Distribute the negative Sign

Add like terms

Write in standard form

2 2(1 ) (3 2 5)x x x

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