Adding, Subtracting and Multiplying Polynomials

Add, Subtract, and Multiply Polynomials

I Can Add, Subtract, and Multiply Polynomials.

Polynomials

• One term: x, -7x², 5-- monomial

• Two terms: (x+5) , (3x² - 6) --binomial

• Three terms: (x² + 3x - 18), 7x3 + 5x - 2 --Trinomial

• More than 3 terms: polynomial

• Always write them in standard form: Exponents decrease in order.

Multiple Choice

Classify by number of terms:
3x³ – 6x

• Monomial

• Binomial

• Trinomial

• 4-Term Polynomial

Multiple Choice

4x² + 8x - 7 is classified as a...

• Monomial

• Binomial

• Trinomial

• Cubic

Multiple Choice

Which polynomial is written in standard form?

• -3x + 8x² + 9x³ - 11

• 9x³ + 8x² - 3x - 11

• 8x² + 9x³ -11 - 3x

• -11 - 3x + 8x² + 9x³

Adding and Subtracting Polynomials

• Put in standard form first

• Use Algebra tiles if needed

• For addition just combine like terms

• For subtraction change the signs of every value in the parenthesis and just add.

  
  

Subtracting Polynomials

​Adding Polynomials

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

Find the sum.

(2x² + 5x - 7) + (3 - 4x² + 6x)

• 2x² + 3x +1

• -2x² - 11x -4

• 2x²+ 5x -7

• -2x² + 11x -4

Multiple Choice

Use algebra titles to add

(2x² - 4x + 1)

+ (x² + 2x - 2)

• x² - 2x - 2

• 3x² + 2x - 1

• 3x² - 2x - 1

• 3x² - 8x -2

Multiple Choice

Simplify each expression.
(6b³ + 6 - b⁴) - (8b³ - 6b⁴ + 2)

• 4b⁴ - 2b³ + 7

• 5b⁴ - 2b³ + 4

• b⁴ - 2b³ + 7

• 5b⁴ - 2b³ + 7

Multiplying Polynomials

• Distribute any number in front of a ( ) to all numbers inside the ( )

• Use the FOIL method to multiply binomials.

  
  

Multiplying monomials

Using box method:

• Create number of rows and boxes to match # of terms per expression. (2x2 for two Binomials)

• Multiply and combine terms

Box method example

The box method works with different combinations of polynomials.

(image: 4 term polynomial multiplying a Trinomial!)

Multiple Choice

Find the product:

$$\left(5s+2\right)^2$$  

• $$25s^2+4$$  

• $$25s^2+10s+4$$

• $$25s^2+20s+4$$  

• $$5s^2+20s+4$$  

Multiple Choice

(4a + 2)(6a² − a + 2)

• 24a³ + 16a² + 6a + 4

• 24a³ + 8a² + 10a + 4

• 24a³ + 8a² + 6a + 4

• 24a³ - 8a² - 6a + 4

Multiple Choice

Find the product:

(3r-4)(7r-5)

• 21r²-43r+20

• 21r+43r²+9

• 7r+12r

• r+2r

Multiple Choice

6v(2v + 3) 

• 12v+18

• 15v² + 8v

• 12v² + 18v

• 12v² + 18v²

Multiple Choice

(2n + 2)(6n + 1)

• 12n + 2

• 12n² + 2

• 12n² + 12n + 2

• 12n² + 14n + 2