Polynomials

Polynomials

Unit 6

Start

Index

Vocabulary

Intro

Factoring

Adding & Subtracting

Difference of Squares

Distributing & Multiplying

Dividing

Vocabulary:

Vocabulary:

Vocabulary:

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Polynomials Module

Adding & Subtracting Polynomials

Distributing & Multiplying Polynomials

Intro

Intro to Polynomials

• An expression that has one or more terms.
• Can include:
• constants
• variables
• whole number exponents
• CANNOT include:
• division by a variable
• negative exponents
• fractional exponents

Examples of Polynomials

CANNOT have negative exponents!

CANNOT have division by variable!

CANNOT have fractional exponents!

Degree of Polynomial

• The largest exponent of any term in a polynomial

Degree of Polynomial

Standard Form

• Terms based on EXPONENT from biggest to smallest!

Standard Form

Adding Polynomials

1. Identify like terms
1. same base and exponent
2. ADD coefficients

Step 2

Step 1

Subtract Polynomials

1. Identify like terms
1. same base and exponent
2. SUBTRACT coefficients

Step 2

Step 1

Distribute Polynomials:

Distributing just means you take each number/variable outside the group and multiply it by every single number/variable inside the group.

The Box Method!

1. Draw the box/grid
1. rows: number of terms in first part of problem
2. columns: number of terms in second part of problem
2. Multiply outside numbers into each cell
3. If needed, combine like terms inside of cells

Multiplying Polynomials:

Multiplying polynomials is the process of taking every term in one polynomial and multiplying it by every term in the other polynomial.

The Box Method!

1. Draw the box/grid
1. rows: number of terms in first part of problem
2. columns: number of terms in second part of problem
2. Multiply outside numbers into each cell
3. If needed, combine like terms inside of cells

The FOIL Method!

First, Outer, Inner, Last

F - First: Multiply the first term in each set of parentheses.

O - Outer: Multiply the outer terms (the ones of the far ends).

I - Inner: Multiply the inner terms ( the ones in the middle).

L - Last: Multiply the last term in each set of parentheses.

Final STEP!

Factoring Polynomials Module

Factoring by GCF

Factoring

Factoring

Greatest Common Factor (GCF)

The greatest common factor, GCF, is the BIGGEST monomial that divides into each term evenly.

DESMOS hack

Factoring by the GCF

1. Find the GCF
2. Divide each coefficient by the GCF to factor each term
3. Write down factors for each term
4. GCF is on outside; everything else on the inside

Answer

DESMOS hack

Factoring by

1. Does your expression look like
2. Find factors for C
3. Write down factors for C
4. Find the factor pair that ADDs to equal B
5. Use factors to fill in answer formula:

Answer

Factoring by

1. Does your expression look like
2. Multiply A and C
3. Find factors for product of A and C
4. Find the factor pair that adds to B
1. Replace pair with B in original problem to create new pairs
5. Factor the GCF of each pair
6. Rewrite factors

Factor Pairs

Inside #'s

Outside #'s

Answer

Example 1

Factor Pairs

Answer

Polynomials Module Pt. 3

Differenceof Squares

Dividing Polynomials

Difference of Squares

1. Do you have a binomial?
2. Find the square roots of both terms
3. Write factors in this form:

Dividing Polynomials

1. Set up box
2. Put divisor (bottom number/variable) on the outside
3. Put the dividend (top numbers/variables) on the inside
4. Divide outside by each inside term
5. Write as a polynomial

Answer

Factor each pair!

Step 1

1. Identify Like Terms
1. Same base AND same exponent

Example 2

Answer

Example 2

Answer

Example 1

Answer

Inside #'s

Outside #'s

Step 1

1. Identify Like Terms
1. Same base AND same exponent

DESMOS: Find the GCF

Combine Like Terms

DESMOS: Find the GCF

Step 2

1. Subtract coefficients

Step 2

1. Add coefficients

Example 1

Answer

Inside #'s

Outside #'s

Factor each pair!

Adding Polynomials

Subtracting Polynomials

Example 1

Example 2

Example 2

Example 1