1. 2nd Degree Polynomial Function1.
Polynomial Functions
Polynomial functions have multiple terms with bases raised to different powers
The degree of the polynomial function is the highest exponent in the equation
2nd degree and higher polynomials are non-linear functions
F(x) means the output of the function when the input is x. f(x) = y = h(x) = g(x)
2nd Degree Polynomial Function
Term
“Function of x”
“f of x”
Output when
input is x
Exponent
f(x) = 5x2 + 15x + 30
Coefficient
Base

2. Include the sign before the number when you combine like terms2.
Adding and Subtracting Polynomial Expressions
Example 1: Simplify the polynomial expression using distributive property and by combining like terms
2x2 + 6x + 4x2 – 20x
2x2 + 6x + 4x x
Include the sign before the number when you combine like terms
6x2 – 14x

3. THEN, Combine Like Terms2.
Adding and Subtracting Polynomial Expressions
Example 2: Simplify the expression using distributive property and by combining like terms
4( x3 – 5x2) – ( x3 + 3x2)
Distribute FIRST
THEN, Combine Like Terms
4( 1x3 + -5x2 ) + -1( 1x3 + 3x2)
4x x2 + -1x3 + -3x2
3x3 – 23x2

4. Subtract the exponents3.
Exponents Operations Review
Polynomial Operation
Exponent Operation
Adding/Subtracting
(+ / - )
Stays the same
Multiplying
(*)
Add the exponents
Dividing
(/)
Subtract the exponents

5. 4. (x – 5)(x + 3) (x – 5)(x + 3) X2 + 3x – 5x - 15 X2 – 2x – 15
Multiplying
Polynomial Expressions
Example 1: Multiply the polynomial
(x – 5)(x + 3)
Box Method
Distribution Method
(FOIL) x 3
Each box is a product
(multiply) x2 3x
(x – 5)(x + 3) x
-5x
X2 + 3x – 5x - 15
Add up all the boxes
-15 -5
X2 – 2x – 15

6. 4. (2b – 7)(b – 6 ) (2b – 7)(b – 6) 2b2 – 19b + 42 2b2 – 12b – 7b + 42
Multiplying
Polynomial Expressions
Example 2: Multiply the polynomial
(2b – 7)(b – 6 )
Box Method
Distribution Method
(FOIL) 2b -7
Each box is a product
(multiply)
2b2
(2b – 7)(b – 6) b
-7b
-12b
2b2 – 12b – 7b + 42 42 -6
Add up all the boxes
2b2 – 19b + 42

7. 4. (5c + 4)(3c – 4 ) (5c + 4)(3c – 4) 15c2 – 8c – 16
Multiplying
Polynomial Expressions
Example 3: Multiply the polynomial
(5c + 4)(3c – 4 )
Box Method
Distribution Method
(FOIL) 5c 4
Each box is a product
(multiply)
15c2
(5c + 4)(3c – 4) 3c
12c
-20c
15c2 – 20c + 12c – 16
-16 -4
Add up all the boxes
15c2 – 8c – 16

8. 4.
Multiplying
Polynomial Expressions
Example 4: Multiply the polynomial
(4a + 2)(6a2 – a + 2)
Box Method
6a2 -a 2
Each box is a product
(multiply)
24a3 4a
-4a2 8a
12a2 4
-2a 2
Add up all the boxes
24a3 + 8a2 + 6a + 4

9. 5. x2 + bx + c (x )( x ) Polynomial Terms Signs in Factored Form +, +
Factoring
Polynomial Expressions
Sum
Product
x2 + bx + c
(x )( x )
Polynomial Terms
Signs in Factored Form
+, +
(x + ), (x + )
+, -
(x + big), (x - )
-, +
(x - ), (x - )
-, -
(x + ), (x - big)

10. 5. X2 + 6x + 8 (x + )( x + ) (x + 4)( x + 2) Polynomial Terms
Factoring
Polynomial Expressions
Example 1: Factor the polynomial
Sum
Product
X2 + 6x + 8
(x + )( x + )
(x + 4)( x + 2)
Polynomial Terms
Signs in Factored Form
+, +

11. 5. g2 + 7g – 18 (g + big)( x – ) (g + 9)(g – 2) Polynomial Terms
Factoring
Polynomial Expressions
Example 2: Factor the polynomial
Sum
Product
g2 + 7g – 18
(g + big)( x – )
(g + 9)(g – 2)
Polynomial Terms
Signs in Factored Form
+, -
+ (bigger) , -

12. 5. 2h2 – 22h + 48 2(h2 – 11h + 24) 2(h – )(h – ) 2(h – 8)(h – 3)
Factoring
Polynomial Expressions
Example 3: Factor the polynomial
2h2 – 22h + 48
2(h2 – 11h + 24)
2(h – )(h – )
2(h – 8)(h – 3)
Polynomial Terms
Signs in Factored Form
-, +
-, -

13. 5. 5m2 – 4h – 21 (5m – big)(m + ) (2h – 7)(h + 3) Polynomial Terms
Factoring
Polynomial Expressions
Example 3: Factor the polynomial
Sum
Product
5m2 – 4h – 21
(5m – big)(m + )
(2h – 7)(h + 3)
Polynomial Terms
Signs in Factored Form
-, -
+, - (bigger)