9.1 Adding and Subtracting Polynomials

Title: 9.1 Adding and Subtracting Polynomials

EQ: How do you know what terms you can add and subtract, and which you can not?

What is a polynomial?

• The root poly means many

• A polynomial is a mathematical expression with many terms

• Standard form - written in order from biggest exponent to smallest

• once in standard form- the coefficient with the first term is called the Leading Coefficent

  • This is always a NUMBER not a VARIABLE

​Name by the number of TERMS - how many things are being added or subtracted

Naming Polynomials

​Name by the DEGREE- The largest exponent

Multiple Choice

Classify by number of terms:

3x³ – 6x

• Monomial

• Binomial

• Trinomial

• 4-Term Polynomial

Multiple Choice

Classify by number of terms:

3x² – 8x + 1

• Monomial

• Binomial

• Trinomial

• 4-Term Polynomial

Multiple Choice

Classify by number of terms:
9x

• Monomial

• Binomial

• Trinomial

• 4-Term Polynomial

​Like Terms: terms that have the SAME variable(s)

​​Example: 4x and 17x

Combine Like Terms: take multiple like terms and make them one (By ADDING or SUBTRACTING)

​​Another word used is SIMPLIFY.

​Vocabulary - write this in your notes

EXAMPLE

​Simplify: 10 - 4ab + 2 + 8ab

Poll

Is this in standard form?

12x+13x³-10

• Yes

• No

  It should be

  -10+12x+13x³

• No

  It should be

  13x³+12x-10

Multiple Choice

What is the leading coefficient?

3x + 5 + 10x⁴

• 3

• 5

• 10

Multiple Choice

What is the leading coefficient?

10x - 12x²+15

• 10

• 12

• -12

• 15

Multiple Choice

Combine the like terms in the expression: 5y+2+3y+6

• There are no like terms

• 8y+2+6

• 53y+12

• 8y+8

​​Adding Polynomials

​(Finding the sum)

Method 1

• ​Drop the parentheses.

• ​Combine like terms

​

​

​

​

​

​*Start with the highest degree*

​EXAMPLE

​Simplify by performing the given operation

​(3x + 12 - 7y) + (22 - 9x - 13y)

Multiple Choice

Add the polynomials.
(3x³ + 3x² – 4x + 5) + (x³ – 2x² + x – 4)

• 4x³ + 1x² – 3x + 1

• 2x³ + 1x² - 5x + 9

• 6x³ + 1x - 1x² - 3

• 3x⁵ +1x - 1x⁵ - 3x

Multiple Choice

Simplify the expression.
(4a³ - 8a - 4a²) + (7a³ - 7 - 6a)

• 11a³ - 4a² - 14a - 7 

• 5a³ - 4a² - 14a - 7 

• 5a³ - 4a² - 20a - 7 

• 5a³ - 9a² - 20a - 7

Multiple Choice

Simplify:

• 9n³ + 4n

• 7n³ + 6

• -3n³ + 2

• 7n⁶ + 6

Multiple Choice

Find the sum.
(2x² + 5x - 7) + ( 3 - 4x² + 6x)

• 2x² + 3x +1

• -2x² - 11x -4

• 2x² + 5x -7

• -2x² + 11x -4

​Subtracting Polynomials

​Finding the difference

​Method 1

• ​Distribute the negative sign to each term in the 2nd set of parenthesis.

• ​Add/combine like terms like before!

​

​

​

​*Start with the highest degree*

​

Multiple Choice

(x³-x²+4) - (3x³-2x²+3)

• -2x³-3x²+7

• -2x³+x²+1

• 2x³-3x³-1

• 4x³-3x²+7

Multiple Choice

Add or Subtract to Simplify:
(x⁵ + x³) - (6x - x³ + 6x⁵)

• -5x⁵ + 2x³ - 6x

• 7x⁵ - 6x

• -5x³ + 2x² - 6x

• -5x⁵ - 6x

Multiple Choice

Add or Subtract to Simplify:
(4x²+ x) - (x²+ 2x)

• 3x² - x

• 4x² + 2x

• 3x² + 3x

• 3x² + 2x

Multiple Choice

What is the perimeter of the triangle shown?

• 9r²+r-5

• 9r⁴+r²-4

• 9r²-r+4

• 9r²+r-4

Poll

After today's review, how would you rate your understanding of adding and subtracting polynomials?

• 4

  I can explain how to do this. I can teach others. I am an expert.

• 3

  I can do this independently. I have a good understanding.

• 2

  I can do this with help or an example. There are parts I still do not understand

• 1

  I do not understand yet, but am starting to learn. I need help learning this.

9.1 Homework

Pg.111 #2-26 even