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)