Any questions on the Section 6'2B homework

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Any questions on the Section 6.2B homework?
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Now please CLOSE YOUR LAPTOPS and turn off and
put away your cell phones.
Sample Problems Page Link (Dr. Bruce Johnston)
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Section 6.3 and 6.4

• Complex Fractions and
• Dividing Polynomials

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Key Concepts from Section 6.3

• Complex rational expressions (complex fractions)
  are rational expressions whose numerator,
  denominator, or both contain one or more rational
  expressions.

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• Example of a complex fraction
• 10
• 3x
• 5
• 6x
• Solution view as a division problem
• 10 5 10 6x 4
• 3x 6x 3x 5

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Problem from todays homework
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Problem from todays homework
Note This one requires that you first combine
the added or subtracted pairs of rational
expressions into single rational expressions with
a common denominator.
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Section 6.4

• Dividing a polynomial by a monomial
• Divide each term of the polynomial separately by
  the monomial.

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Problem from todays homework
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• Dividing a polynomial by a polynomial other than
  a monomial uses a long division technique that
  is similar to the process known as long division
  in dividing two numbers.
• This process is reviewed in detail on the next
  slide, but first, well work these two simpler
  examples on the whiteboard
• 1). 225 9
• 2). 231 9
• Question How can you check your answers on long
  division problems?

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Example Long Division with integers
Divide 43 into 72.
Multiply 1 times 43.
Subtract 43 from 72.
Bring down 5.
Divide 43 into 295.
Multiply 6 times 43.
Subtract 258 from 295.
Bring down 6.
Divide 43 into 376.
Multiply 8 times 43.
Subtract 344 from 376.
Nothing to bring down.
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• As you can see from the previous example, there
  is a pattern in the long division technique.
• Divide
• Multiply
• Subtract
• Bring down
• Then repeat these steps until you cant bring
  down or divide any longer.
• We will incorporate this same repeated technique
  with dividing polynomials.

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Now you try it (And dont forget to check your
answer!)

• Divide 3471 by 6 using long division.
• Then check your answer.
• Do this in your notebook now, and make sure you
  ask if you have questions about any step. This
  will be crucial to your understanding of long
  division of polynomials.

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Divide 7x into 28x2.
Multiply 4x times 7x3.
Subtract 28x2 12x from 28x2 23x.
Bring down -15.
Divide 7x into 35x.
Multiply -5 times 7x3.
Subtract 35x15 from 35x15.
Nothing to bring down.
So our answer is 4x 5.
Check Multiply (7x 3)(4x 5)
and see if you get 28x2 23x - 15.
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Now you try it (And dont forget to check your
answer!)

• Divide 6x2 x 2 by 3x 2 using
  long division.
• Then check your answer.
• Do this in your notebook now, and make sure to
  ask if you have questions about any step.
• ANSWER 2x 1

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Divide 2x into 4x2.
Multiply 2x times 2x7.
Subtract 4x2 14x from 4x2 6x.
Bring down 8.
Divide 2x into 20x.
Multiply -10 times 2x7.
Subtract 20x70 from 20x8.
78
Nothing to bring down.
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How do we check this answer?
Final answer 2x 10 78 .
2x - 7
78
How to check Calculate (2x 7)(2x 10)
78. If it comes out to 4x2 6x 8,
then the answer is correct.
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Now you try it (And dont forget to check your
answer!)

• Divide 15x2 19x 2 by 3x 5
  using long division.
• Then check your answer.
• Do this in your notebook now, and make sure you
  ask if you have questions about any step.
• Answer 5x 2 8 .
• 3x 5

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Problem from todays homework
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Problem from todays homework
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Something to be aware of on Problem 14 in
todays homework

• The online Help Me Solve This instructions for
  this problem demonstrate a method called
  Synthetic Division. (We are not covering this
  method in class, because it is only useful in the
  cases where the divisor is of the form x c.)
• You will get the same answer using the long
  division method, so this is what we expect you to
  use to solve this problem. (If you are already
  familiar with synthetic division, youre welcome
  to use it in those cases where it is applicable,
  but we arent expecting you to learn it on your
  own.)

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Reminder

• This homework assignment
• on section 6.4 and 6.3 is due
• at the start of
• next class period.

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You may now OPEN your LAPTOPS and begin working
on the homework assignment.