Adding, Subtracting, and Multiplying Polynomials

1
Chapter 6.3

• Adding, Subtracting, and Multiplying Polynomials
• By Candace W.

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2
Outline

• Adding Polynomials
• Adding polynomials Explanation
• Adding polynomials Examples and Reminders
• Quiz
• Answers
• Subtracting polynomials
• Subtracting polynomials Explanation
• Subtracting polynomials Examples and Reminders
• Quiz
• Answers
• Multiplying polynomials
• Multiplying polynomials Explanation
• Multiplying polynomials Examples and Reminders
• Special Product Patterns
• Quiz
• Answers
• Chapter 6.3 Test
• Chapter 6.3 Answers

3
Adding Polynomials

• 3x³2x²-x-7
• x³-10x² 8
• 4x³-8x²-x1

4
Adding Polynomials explanation

• Vertical
• I find writing your problem vertically is much
  easier because you can see what you are dealing
  with for both parts of the problem. If they
  already are not done so, then put the the numbers
  in largest to smallest order by how many of a
  variable they have. Then all you have to do is
  add alike terms going down the problem. If there
  is not a variable in the second part of the
  problem then leave a spot or just bring it down
  in its respective place.

• Horizontal
• I personally do not like solving polynomials
  horizontally. When they are placed horizontally
  the first part of the problem will be in one set
  of parentheses and the second part in another set
  or parentheses. Make sure they are in order by
  the number of variables they have. Then add
  alike terms and simplify if you have more than
  one of the same terms in your answer.

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Examples and Reminders

• Add all alike terms (x³, x², x, etc)
• Bring down alone terms into answer.

6
Adding polynomials Quiz.
Click here for Answers

• (8x²1) (3x²-2)
• (50x-3) (8x³7x²x4)
• (10x-37x²) (x³-2x17)
• 8x (14x3-41x²x³)
• (16-13x) (10x-11)

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7
Adding polynomials Answers

• 11x²-1
• 8x³7x²51x1
• x³7x²8x14
• X³-41x²22x3
• -3x5

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Subtracting Polynomials

• 8x³-3x²-2x9
• - 2x³6x²-x1
• 6x³-9x²-x8

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Subtracting Polynomials Explanation

• Add the opposite
• Change all signs to their opposites in the second
  half of the problem then add like terms.

• Subtract
• Subtract all like terms.

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Examples and Reminders

• When adding opposites change all signs in 2nd
  part of problem.
• Double check your subtraction.

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Subtracting Polynomials Quiz

• (9x³-4x²8x) (7x³-3x7)
• (6x²-19x5) (19x²-4x9)
• (3x³10x5) (x³-4x6)
• (x²-6x5) (x²x-2)
• (10x³-4x²3x) (x³-x²1)

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Click for Answers
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Subtracting Polynomials Answers

• 2x³x²11x-11
• -13x²-15x-4
• 2x³14x-1
• -7x7
• 9x³-3x²3x1

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Multiplying Polynomials

• -x²2x4
• X x- 3 3x²-6x-12
• -x³2x²4x__
• -x³5x²-2x-12

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Multiplying Polynomials Explanation

• Vertically
• To multiply Polynomials, each term of the first
  part must be multiplied by each term of the
  second part.
• Just like Multiplying Larger numbers in
  Elementary School.

• Horizontally
• Each part of the first polynomial must be
  multiplied to the second.
• Tree Binomials
• Multiply two first, then multiply the answer to
  the third polynomial.

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Special Product Patterns

• Sum and Difference
• (ab)(a-b)a²-b²
• Square of a Binomial
• (ab)²a²2abb²
• (a-b)²a²-2abb²
• Cube of a Binomial
• (ab)³a³3a²b3ab²b³
• (a-b)³a³-3a²b3ab²-b³

• Example
• (x3)(x-3) x²-9
• (y4)²y²8y16
• (3t²-2)²9t4-12t²4
• (x1)³x³3x²3x1
• (p-2)³p³-6p²12p-8

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Examples and Reminders

• Multiply each term of the 1st polynomial by each
  of the 2nd terms.
• Check your multiplication.
• If a binomial is squared (²) then write the
  binomial again. (x6)²(x6)(x6)

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Multiplying Polynomials Quiz.

• 5x(3x²-x3)
• 10x²(x-5)
• (x1)(5x³-x²x-4)
• (x-5)(x5)
• (2x5)(3x³-x²x)

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Click for answers
18
Multiplying Polynomials Answers

• 15x³-5x²15x
• 10x³-50x²
• 5x44x³-3x-4
• X²-25
• 6x413x³-3x²5x

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Chapter 6.3 Test
Click for Answers

• (x4)²
• (x9)(x-2)(x7)
• (x6)(x5)
• (x²-6x5) (x²x-2)
• (16-13x) (10x-11)
• (7y-x)²
• (x3)(x-4)(x7)
• 5x²(x-3)
• 3x (7x2-6x²2x³)
• (7x³-1) (10x³4x²-2x4)

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Chapter 6.3 Answers

• x²8x16
• x³14x²31x-126
• x²11x30
• 2x²-5x3
• -23x27
• 49y²-14xyx
• x³6x²-19x-84
• 5x³-15x²
• 2x³-6x²10x2
• 3x³4x²-2x-5