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# Adding and Subtracting Polynomials

Math Project

#### Transcript of Adding and Subtracting Polynomials

Adding and Subtracting Polynomials by Eva Sauve' and Angel See Combining like terms also goes for negative

terms, so when you combine them you subtract instead of adding together. When adding vertically:

5x +4x+1

+2x +5x+2

____________

7x +9x+3 More Problems 1. (2x -x)+(x +3x+1) 3x +5-7x +12 Like Terms When adding or subtracting polynomials,

you have to combine like terms.

Two or more terms can be combined when

they have the same variable with the same

exponent. What's a Polynomial? Subtracting Vertical and Horizontal Form Try These Problems: A polynomial is a monomial or the sum or difference of monomials.

Monomials, binomials, and trinomials

are all polynomials. Monomials

A number by itself or a number with one variable. It has only one term.

Examples:

5 or 5x Examples Binomials

The sum or difference of two monomials, or terms. 2 3x+23 8x -42 Examples: 2 Trinomials A polynomial with three terms either added and/or subtracted. Examples:

x +5x-2

-x -4x+5 2 2 Examples: 3x+5+7x 33y +4x+62y 2 2 8z+z-4z 15m +6m +2m 3 2 3 15m +6m +2m 3 2 3 Combine the terms. 15m +2m +6m 3 2 3 17m +6m 2 Since 15m and 2m are like terms, they

can be combined. The other term, 6m ,

doesn't have any like terms, so it's not

combined. When 15m and 2m are added together, it equals 17m , making the answer 17m +6m . 3 3 2 3 3 3 3 2 2 2 Rearrange these terms 3x +5-7x +12 2 2 3x -7x +5+12 2 2 -4x +17 2 1. 4z -8+16z +2 4 4 2. 2x +7y -x -y 8 8 8 8 3. 2x +3x +x Make sure the answer is in standard form; the term with the highest degree being first. 3 Highest degree Second highest degree Answers: 1. 20z -6 4 2. x +6y 8 8 3. 5x +x 2 2 2 2 2 2 When adding horizontally:

(5x +4x+1)+(2x +5x+2)

=(5x +2x )+(4x+5x+)+(1+2)

=7x +9x+3 2 2 2 2 2 Just like adding regular numbers Find like terms Regroup 2. (4b +8b)+(3b +6b-7b +b) 3. 2x +6

-4x

------- 2 2 5 5 5 2 2

1. 3x +2x-1

2. 15b

3. -2x +6 2 2 Answers Word Problem The length of a rectangle is represented by 4a+3b, and its width is represented by 7a-2b. Write a polynomial for the perimeter of the rectangle. Answer to Word Problem: 22a-2b Thanks for Watching!!!!!!!!! Special thanks to Ms. Fredenburg

Full transcriptterms, so when you combine them you subtract instead of adding together. When adding vertically:

5x +4x+1

+2x +5x+2

____________

7x +9x+3 More Problems 1. (2x -x)+(x +3x+1) 3x +5-7x +12 Like Terms When adding or subtracting polynomials,

you have to combine like terms.

Two or more terms can be combined when

they have the same variable with the same

exponent. What's a Polynomial? Subtracting Vertical and Horizontal Form Try These Problems: A polynomial is a monomial or the sum or difference of monomials.

Monomials, binomials, and trinomials

are all polynomials. Monomials

A number by itself or a number with one variable. It has only one term.

Examples:

5 or 5x Examples Binomials

The sum or difference of two monomials, or terms. 2 3x+23 8x -42 Examples: 2 Trinomials A polynomial with three terms either added and/or subtracted. Examples:

x +5x-2

-x -4x+5 2 2 Examples: 3x+5+7x 33y +4x+62y 2 2 8z+z-4z 15m +6m +2m 3 2 3 15m +6m +2m 3 2 3 Combine the terms. 15m +2m +6m 3 2 3 17m +6m 2 Since 15m and 2m are like terms, they

can be combined. The other term, 6m ,

doesn't have any like terms, so it's not

combined. When 15m and 2m are added together, it equals 17m , making the answer 17m +6m . 3 3 2 3 3 3 3 2 2 2 Rearrange these terms 3x +5-7x +12 2 2 3x -7x +5+12 2 2 -4x +17 2 1. 4z -8+16z +2 4 4 2. 2x +7y -x -y 8 8 8 8 3. 2x +3x +x Make sure the answer is in standard form; the term with the highest degree being first. 3 Highest degree Second highest degree Answers: 1. 20z -6 4 2. x +6y 8 8 3. 5x +x 2 2 2 2 2 2 When adding horizontally:

(5x +4x+1)+(2x +5x+2)

=(5x +2x )+(4x+5x+)+(1+2)

=7x +9x+3 2 2 2 2 2 Just like adding regular numbers Find like terms Regroup 2. (4b +8b)+(3b +6b-7b +b) 3. 2x +6

-4x

------- 2 2 5 5 5 2 2

1. 3x +2x-1

2. 15b

3. -2x +6 2 2 Answers Word Problem The length of a rectangle is represented by 4a+3b, and its width is represented by 7a-2b. Write a polynomial for the perimeter of the rectangle. Answer to Word Problem: 22a-2b Thanks for Watching!!!!!!!!! Special thanks to Ms. Fredenburg