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Polynomial Addition:

Like Terms

To add polynomials, we must CombineCombine Like TermsLike Terms

Say we want to add these two polynomials:x2 - 3x + 4 and 5x2 - 2x - 2

x2 + 5x2

6x6x22

Like Terms have exactly the same variables with exactly the same powers.

Combine Like Terms by adding or subtracting the coefficients, but keep the variables (and powers) the same.

(Use the sign rules of integers to determine whether to add or subtract)

These terms both havex2, so they are like terms

To add polynomials, we must CombineCombine Like TermsLike Terms

Now add the next set of like terms:x2 - 3x + 4 and 5x2 - 2x - 2

-3x - 2x

6x6x22

Like Terms have exactly the same variables with exactly the same powers.

Combine Like Terms by adding or subtracting the coefficients, but keep the variables (and powers) the same.

(Use the sign rules of integers to determine whether to add or subtract)

- 5x- 5x

These terms each have an x, so they are like terms

To add polynomials, we must CombineCombine Like TermsLike Terms

Now add the last set of like terms:x2 - 3x + 4 and 5x2 - 2x - 2

+4 - 2

6x6x22

Like Terms have exactly the same variables with exactly the same powers.

Answer: 6x2 - 5x + 2

- 5x- 5x

These terms are constants(numbers with no variables),

so they are like terms

+ 2+ 2

Horizontal Method

One method of adding polynomials is called the

Horizontal MethodHorizontal Method

Add 2x2 - x - 7 and -x2 + 3x - 4, use the Horizontal Method:

Write the second polynomial in

parentheses with a plus sign between

them

2x2 - x - 7 + ( -x2 + 3x - 4)+ 1

Distribute the +1

2x2 - x - 7 - x2 +3x - 4

2x2 - x2

xx22

Combine Like Terms by adding or subtracting the coefficients, but keep the variables (and powers) the same.

(Use the sign rules of integers to determine whether to add or subtract)

These terms both havex2, so they are like terms

2x2 - x - 7 - x2 + 3x - 4

Horizontal Method: Horizontal Method: Polynomial Addition

Now add the first set of like terms:

Horizontal Method: Horizontal Method: Polynomial Addition

Now add the next set of like terms:2x2 - x - 7 - x2 + 3x - 4

xx22

-x + 3xThese terms each have an x, so they are like terms

+ 2x+ 2x

-7 - 4

xx22

Answer: x2 + 2x - 11

+ 2x+ 2x

These terms are constants(numbers with no variables), so they are like terms

- 11- 11

Horizontal Method: Horizontal Method: Polynomial Addition

Now add the next set of like terms:2x2 - x - 7 - x2 + 3x - 4

Practice Problems: (Hit enter to see the answers)Add using the Horizontal Method

1) -6x2 + 2x + 1 and 3x2 - x + 2 5) 5x + 2x - 3 and 4x + 2

2) 5xy + 4x and -3xy - 12x 6) -3y2 + 2y and y2 + y - 1

3) 4ab + 2a2b and 3ab 7) 2xy - 5x and - 3xy + 6x - 7

4) 3x2y +4x3y and - x3y + 2x2y 8) -17x + 6 and 3x - 6

Answers:1) -3x2 + x + 32) 2xy - 8x3) 2a2b + 7ab4) 3x3y + 5x2y5) 11x - 16) -2y2 + 3y - 17) -xy + x - 78) -14x

Vertical Method

Add 4x2 + 3x - 6 and 2x2 - 5x + 4, use the Vertical Method:

4x2

+ 2x2

Write the two polynomials so

that the like terms are stacked on

top of each otherThese terms both have

x2, so they are like terms

Vertical Method: Vertical Method: Polynomial Addition

4x2

+ 2x2

Write the two polynomials so that the like terms are stacked on top of each otherThese terms both have an

x, so they are like terms

+ 3x

- 5x

Add 4x2 + 3x - 6 and 2x2 - 5x + 4, use the Vertical Method:

Vertical Method: Vertical Method: Polynomial Addition

4x2

+ 2x2

Write the two polynomials so

that the like terms are stacked on

top of each otherThese terms are constants, so they are like terms

+ 3x

- 5x - 6

+ 4

Add 4x2 + 3x - 6 and 2x2 - 5x + 4, use the Vertical Method:

Vertical Method: Vertical Method: Polynomial Addition

Now draw a line under the whole thing and add the

coefficients.

4x2

+ 2x2

+ 3x

- 5x - 6

+ 4

6x2 - 2x - 2ANSWER = ANSWER =

Add 4x2 + 3x - 6 and 2x2 - 5x + 4, use the Vertical Method:

Vertical Method: Vertical Method: Polynomial Addition

Add x2 + 2 and 6x2 - 5x - 3, use the Vertical Method:

Write the two polynomials so

that the like terms are stacked on

top of each other

These terms both havex2, so they are like terms

x2

+ 6x2

Vertical Method: Vertical Method: Polynomial Addition

Add x2 + 2 and 6x2 - 5x - 3, use the Vertical Method:

x2

+ 6x2

+ 0x - 5x

(no x term?)

Solution: Solution: Write in a zero where there

are missing terms. (Or you can leave a blank spot)

A problem that comes up when using the Vertical

Method is that sometimes there are terms missing.

Vertical Method: Vertical Method: Polynomial Addition

Add x2 + 2 and 6x2 - 5x - 3, use the Vertical Method:

Write the two polynomials so

that the like terms are stacked on

top of each other

These terms are constants, so they are like terms

x2

+ 6x2

+ 2

- 3 + 0x - 5x

Vertical Method: Vertical Method: Polynomial Addition

Now draw a line under the whole thing and add the

coefficients.

7x2 - 5x - 1ANSWER = ANSWER =

- 5x

x2

+ 6x2

+ 0x + 2

- 3

Add x2 + 2 and 6x2 - 5x - 3, use the Vertical Method:

Vertical Method: Vertical Method: Polynomial Addition

Suggestions for other situations:Suggestions for other situations:SituationSituation SolutionSolution

1. A term has no coefficient showing Write a “1” in front of it

Example: x2 + 3x + 1 1x2 + 3x + 1

2. There are more than two like terms Stack (or group) all like terms together Ex: 2x + 6x - 3 and 4x + 5 (2x + 6x + 4x) + (-3 + 5)

3. There are many missing terms Write in zeros for each of themEx: 5x3 - 2x and 4x4 + 3x2 + x - 6 0x4 + 5x3 + 0x2 - 2x + 0

4x4 + 0x3 + 3x2 + 1x - 64x4 + 5x3 + 3x2 + 1x - 6

4. Subtraction problem Distribute the (-1) before working the problem.

x2 + 3x + 1 - (2x2 + 6x - 2) x2 + 3x + 1 - 2x2 - 6x + 2

Practice Problems: (Hit enter to see the answers)Add using the Vertical Method

1)-6x2 + 2x + 1 and 3x2 - x + 2 5) 5x + 2x - 3 and 4x + 2

2) 5y + 4x and -3y - 12x 6) -3y2 + 2y and y2 + y - 1

3) 4ab + 2a2 and 3ab 7) 2xy - 5x and - 3xy + 6x - 7

4) 3x2y +4xy and - xy + 2x2y 8) -17x2 + 6 and 3x - 6

Answers:1) -3x2 + x + 32) 2y - 8x3) 7ab + 2a2

4) 5x2y+ 3xy 5) 11x - 16) -2y2 + 3y - 17) -xy + x - 78) -17x2 + 3x

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