4.2 Notes Add Sub Multiply Polynomials

4.2 Polynomials

Add subtract and multiply polynomials.

These are your notes for 4.2. You need to write examples in your notebook; whatever you need that will help you with HW and the quiz.

My hope is that most of this is review, but if you need help make sure you come aske me.

Polynomials

• One term: Monomial examples: x -7x² 5

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

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

• 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 Polynomials

• Put in standard form first if it is helpful for you

• For addition just combine like terms - Put the ones that look a like together

• Make sure to pay attention to the sign in front of the number + / -

  
  

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

Combine (3x - 4) + (12x + 10)

• x - 12

• 15x + 6

• 36x + 40

• 17x + 9,000

Multiple Choice

Find the sum.

(2x² + 5x - 7) + (3 - 4x² + 6x)

• 2x² + 3x +1

• -2x² - 11x -4

• 2x²+ 5x -7

• -2x² + 11x -4

To subtract polynomials

See how the subtraction is changed to adding and the negative is distributed to everything in the second ( ):

You try: Here are some multiple choice practice problems for you to make sure that you understand adding and subtracting. If you dont get it after these, make sure you come ask me for help.

Multiple Choice

Subtract the polynomials:

$$\left(x^2-3x+7\right)-\left(6x^2+4x+12\right)$$  

• $$7x^2-7x-5$$  

• $$-5x^2-7x-5$$  

• $$-5x^2+7x+5$$  

• $$-4x^2-22x$$  

Multiple Choice

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

• 4b⁴ - 2b³ + 7
• 5b⁴ - 2b³ + 4
• b⁴ - 2b³ + 7
• 5b⁴ - 2b³ + 7

Multiple Choice

Simplify (2x + 5y - z) + (-6x - 4y + 7z)

• -4x +6y + 6z

• 4x + y + 6z

• -4x - y + 6z

• -4x + y + 6z

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

Subtract the polynomials.

(2x + 5y) - (3x - 2y)

• -x + 3y

• -x + 7y

• 5x + 7y

• 7xy + 1xy

Multiple Choice

6v(2v + 3) 

• 12v+18
• 15v² + 8v
• 12v² + 18v
• 12v² + 18v²

​FOIL Method

​First

​

​Outer

​

​Inner

​

​Last

Multiple Choice

(3x − 6)(7x + 7)

• 21x² − 63x + 42

• 21x² − 21x − 42

• 21x² − 42

• 21x² + 63x + 42

Multiple Choice

(2x - 1)(x + 2)

• 2x² + 3x - 2

• 2x² - 5x - 2

• 2x² + 3x + 2

• 2x² - 5x + 2

Multiple Choice

Multiply 7x²y³ (2x⁴y⁵+6xy³)

• 14x⁸y¹⁵+42x²y⁹

• 9x⁶y⁸+13x³y⁶

• 14x⁶y⁸+42x³y⁶

• 14x⁶y⁸+42x²y⁶

Multiple Choice

Simplify:

2x ( -2x -3)

• -4x - 3

• x² - 3

• -4x² - 6x

• -4x - 6

Binomial * Trinomial

Multiple Choice

(x + 1) (x² - 2x + 1)

• x³ - x² -x + 1

• x³ - 2x + 2

• x³ + x² + x + 1

• x³ - 3x² - 3x + 1

Multiple Choice

$$\left(3x-3\right)\left(4x^2-2x-5\right)$$

• $$12x^3-18x^2-9x+15$$

• $$12x^3+6x^2+21x-15$$

• $$12x^3+18x^2+9x-15$$

• $$12x^3+6x^2-9x+15$$

Write these down in your notes

Multiple Choice

(x+5)²

• x²+25
• 2x+10
• x²+10x+25
• 12x

Multiple Choice

(x+10)(x-10)

• x²  - 100
• x² + 100
• x² + 20x - 100
• x² -20x + 100

Multiple Choice

(5x+2)(x²-3x+6)

• 5x³ - 17x² +24x +12
• 5x³ + 17x² - 24x +12
• 5x³ - 13x² + 24x +12
• 5x³ +13x² - 24x - 12

Multiple Choice

(x-3)²

• x²-6x+9
• x² - 9
• x² + 9
• x² 

Multiple Choice

(2x − 3)(2x + 3)

• 4x² − 12x + 9
• 4x² − 9
• 4x² + 9
• 4x² + 6x − 9

Multiple Choice

$$\left(4p+1\right)^2$$  

• 16p² + 1
• 16p² − 1
• 16p² − 8p + 1
• 16p² + 8p + 1

Multiple Choice

What is the Perimeter?

• 3x - 3 inches

• 6x - 6 inches

• 3x - 6 inches

• 6x - 3 inches

Multiple Choice

What is the Area?

• $$2x^2-3x-18$$ sq, in.

• $$2x^2+3x+18$$ sq. in.

• $$2x^2+9x-18$$ sq. in.

• $$2x^2-9x-18$$ sq. in.

Multiple Choice

(4x+1)+(5x−2)

• 20x² - 2

• 20x² − 3x - 2

• 9x² − 1

• 9x − 1

Multiple Choice

(4x+1) - (5x−2)

• 9x + 3

• 20x² − 3x - 2

• x² + 3

• -x + 3

Multiple Choice

(4x+1)(5x−2)

• 20x² + 3x − 2
• 20x² − 11x + 5
• 20x² − 18x + 2
• 20x² − 3x − 2

Multiple Choice

#10: What is the product of the expression below?

• Option 1

• Option 2

• Option 3

• Option 4

Multiple Choice

#11: What is the product of the expression below?

• Option 1

• Option 2

• Option 3

• Option 4

Multiple Choice

#16: What is area of the square shown below?

• Option 1

• Option 2

• Option 3

• Option 4

Homework

Big Ideas

If you got done you can go to big ideas and start your HW now, if not you can do this for homework. Due by next class.