Polynomials Math
1. Polynomial Functions
f(x) = 5x2 + 15x + 30Coefficient Base
ExponentTerm“Function of x”
“f of x”
Output when
input is x
• 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
Polynomials Math
2. Adding and Subtracting Polynomial Expressions
Example 1: Simplify the polynomial expression using distributive property and by combining like terms
6x2 – 14x
2x2 + 6x + 4x2 + -20x
2x2 + 6x + 4x2 – 20x
Include the sign before the
number when you combine
like terms
Polynomials Math
Example 2: Simplify the expression using distributive property and by combining like terms
4( x3 – 5x2) – ( x3 + 3x2)
3x3 – 23x2
4( 1x3 + -5x2 ) + -1( 1x3 + 3x2)
4x3 + -20x2 + -1x3 + -3x2
2. Adding and Subtracting Polynomial Expressions
Distribute FIRST
THEN, Combine
Like Terms
Polynomials Math
3. Exponents Operations Review
Polynomial Operation
Exponent Operation
Adding/Subtracting
(+ / - )
Stays the same
Multiplying
(*)
Add the exponents
Dividing
(/)
Subtract the exponents
Polynomials Math
Example 1: Multiply the polynomial
(x – 5)(x + 3)
4. Multiplying
Polynomial Expressions
Box Method
x
-5
x 3Each box
is a product (multiply)
x2 3x
-15-5xAdd up all the boxes
Distribution Method(FOIL)
(x – 5)(x + 3)
X2 + 3x – 5x - 15
X2 – 2x – 15
Polynomials Math
(2b – 7)(b – 6 )Box Method
b
-6
2b -7
Each box is a
product (multiply)
2b2-7b
42-12bAdd up all the boxes
Distribution Method(FOIL)
(2b – 7)(b – 6)
2b2 – 12b – 7b + 42
2b2 – 19b + 42
Example 2: Multiply the polynomial4. Multiplying
Polynomial Expressions
Polynomials Math
(5c + 4)(3c – 4 )Box Method
3c
-4
5c 4
Each box is a
product (multiply)
15c212c
-16-20cAdd up all the boxes
Distribution Method(FOIL)
(5c + 4)(3c – 4)
15c2 – 20c + 12c – 16
15c2 – 8c – 16
Example 3: Multiply the polynomial4. Multiplying
Polynomial Expressions
Polynomials Math
(4a + 2)(6a2 – a + 2)Box Method
4a
2
6a2 -a
Each box is a
product (multiply)
24a3-4a2
-2a12a2
Add up all the boxes
24a3 + 8a2 + 6a + 4
Example 4: Multiply the polynomial4. Multiplying
Polynomial Expressions
2
8a
4
Polynomials Math
x2 + bx + c
5. Factoring
Polynomial Expressions
Sum Product
(x )( x )
Polynomial Terms
Signs in Factored Form
+, + (x + ), (x + )
+, - (x + big), (x - )
-, + (x - ), (x - )
-, - (x + ), (x - big)
Polynomials Math
Example 1: Factor the polynomial
X2 + 6x + 8
5. Factoring
Polynomial Expressions
Sum Product
(x + )( x + )
Polynomial Terms
Signs in Factored Form
+, + +, +
(x + 4)( x + 2)
Polynomials Math
Example 2: Factor the polynomial
g2 + 7g – 18
5. Factoring
Polynomial Expressions
Sum Product
(g + big)( x – )
Polynomial Terms
Signs in Factored Form
+, - + (bigger) , -
(g + 9)(g – 2)
Polynomials Math
Example 3: Factor the polynomial
2(h2 – 11h + 24)
5. Factoring
Polynomial Expressions
2(h – )(h – )
Polynomial Terms
Signs in Factored Form
-, + -, -
2(h – 8)(h – 3)
2h2 – 22h + 48
Polynomials Math
Example 3: Factor the polynomial
5m2 – 4h – 21
5. Factoring
Polynomial Expressions
Sum Product
(5m – big)(m + )
Polynomial Terms
Signs in Factored Form
-, - +, - (bigger)
(2h – 7)(h + 3)
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