SOLUTION: Find the quotient using long division. (I have to show work.) 8m^3 +38^2 -6m +20/m+5 Answers being: (A)8m^2+2m+4 (B)m^2+2m+8 (C)8m^2-2m+4 (D) m^2+3m+4 Second question: Mult

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Question 22169: Find the quotient using long division. (I have to show work.)
8m^3 +38^2 -6m +20/m+5
Answers being: (A)8m^2+2m+4 (B)m^2+2m+8 (C)8m^2-2m+4 (D) m^2+3m+4
Second question:
Multiply: (3y+11)(8y^2-2y-9) (I have to show work.)
Answers being: (A) 24y^3-6y^2-27y+11
(B) 112y^2-28y-126
(C) 24y^3+28y^2-49y-99
(D) 24y^3+94y^2+49y+99
Thank you.
Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!
Find the quotient using long division. (I have to show work.)

(8m^3 + 38m^2 - 6m + 20)/(m + 5)

Answers being: (A)8m^2+2m+4 (B)m^2+2m+8 (C)8m^2-2m+4 (D) m^2+3m+4 
Second question:


Start with this:

       ----------------------
  m + 5) 8m3 + 38m2 - 6m + 20

Divide m into 8m3, which amounts to 8m3/m or 8m2. Place that above
the line above 38m2:

                8m2
       ----------------------
  m + 5) 8m3 + 38m2 - 6m + 20

Multiply 8m2 by the 5, getting 40m2 and place it under the 38m2

                8m2
       ----------------------
  m + 5) 8m3 + 38m2 - 6m + 20 
             + 40m2

Multiply 8m2 by the m, getting 8m3 and place this under the other 8m3

                8m2
       ----------------------
  m + 5) 8m3 + 38m2 - 6m + 20 
         8m3 + 40m2

Draw a line underneath

                8m2
       ----------------------
  m + 5) 8m3 + 38m2 - 6m + 20 
         8m3 + 40m2
         ----------

Subtract vertically by mentally changing the sign of the 
8m3 and the 40m2 and adding, getting 0 and -2m2.  Write only
the -2m2

                8m2
       ----------------------
  m + 5) 8m3 + 38m2 - 6m + 20 
         8m3 + 40m2
         ----------
               -2m2

Bring down the -6m

                8m2
       ----------------------
  m + 5) 8m3 + 38m2 - 6m + 20 
         8m3 + 40m2
         ----------
               -2m2 - 6m 

Divide m into -2m2, which amounts to -2m2/m or -2m. Place that above
the line above " - 6m ":

                8m2 - 2m
       ----------------------
  m + 5) 8m3 + 38m2 - 6m + 20 
         8m3 + 40m2
         ----------
               -2m2 - 6m 

Multiply -2m by the 5, getting -10m and place it under the "- 6m"

                8m2 -  2m
       -----------------------
  m + 5) 8m3 + 38m2 -  6m + 20 
         8m3 + 40m2
         ----------
               -2m2 -  6m 
                    - 10m

Multiply -2m by the m, getting -2m2 and place this under the other -2m2  

                8m2 -  2m
       -----------------------
  m + 5) 8m3 + 38m2 -  6m + 20 
         8m3 + 40m2
         ----------
               -2m2 -  6m 
               -2m2 - 10m

Draw a line underneath:

                8m2 -  2m
       -----------------------
  m + 5) 8m3 + 38m2 -  6m + 20 
         8m3 + 40m2
         ----------
               -2m2 -  6m 
               -2m2 - 10m
               ----------

Subtract vertically by mentally changing the sign of the -2m2 and the -10m
and adding, getting 0 and 4m.  Write only the 4m.

                8m2 -  2m
       -----------------------
  m + 5) 8m3 + 38m2 -  6m + 20 
         8m3 + 40m2
         ----------
               -2m2 -  6m 
               -2m2 - 10m
               ----------
                       4m

Bring down the +20

                8m2 -  2m
       -----------------------
  m + 5) 8m3 + 38m2 -  6m + 20 
         8m3 + 40m2
         ----------
               -2m2 -  6m 
               -2m2 - 10m
               ----------
                       4m + 20

Divide m into 4m, which amounts to 4m/m or "+ 4". Place that above
the line above "+ 20":

                8m2 -  2m +  4
       -----------------------
  m + 5) 8m3 + 38m2 -  6m + 20 
         8m3 + 40m2
         ----------
               -2m2 -  6m 
               -2m2 - 10m
               ----------
                       4m + 20

Multiply 4 by the 5, getting +20, and place it under the other + 20

                8m2 -  2m +  4
       -----------------------
  m + 5) 8m3 + 38m2 -  6m + 20 
         8m3 + 40m2
         ----------
               -2m2 -  6m 
               -2m2 - 10m
               ----------
                       4m + 20
                          + 20

Multiply 4 by the m, getting 4m and place this under the other 4m

                8m2 -  2m +  4
       -----------------------
  m + 5) 8m3 + 38m2 -  6m + 20 
         8m3 + 40m2
         ----------
               -2m2 -  6m 
               -2m2 - 10m
               ----------
                       4m + 20
                       4m + 20

Draw a line underneath

                8m2 -  2m +  4
       -----------------------
  m + 5) 8m3 + 38m2 -  6m + 20 
         8m3 + 40m2
         ----------
               -2m2 -  6m 
               -2m2 - 10m
               ----------
                       4m + 20
                       4m + 20
                       -------

Subtract vertically by mentally changing the sign of the 4m and the +20
and adding, getting 0 and 0.  Write only the second 0.

                8m2 -  2m +  4
       -----------------------
  m + 5) 8m3 + 38m2 -  6m + 20 
         8m3 + 40m2
         ----------
               -2m2 -  6m 
               -2m2 - 10m
               ----------
                       4m + 20
                       4m + 20
                       -------
                             0

Since the remainder is 0, the quotient is 8m2 - 2m + 4

So the correct choice is (C)

----------------------------------------------

Multiply: (3y+11)(8y²-2y-9) (I have to show work.) 

  (3y+11)(8y²-2y-9)

Answers being:
(A) 24y^3-6y^2-27y+11
(B) 112y^2-28y-126
(C) 24y^3+28y^2-49y-99
(D) 24y^3+94y^2+49y+99 
Thank you.

Write the second parenthetical expression (8y²-2y-9)
as [(8y²-2y)-9]

(3y+11)[(8y²-2y)-9]

I colored the (8y²-2y) red so you can see that you are using "FOIL"
Consider the parenthetical red factor as just ONE single term.

 FIRSTS    +  OUTERS  +   INNERS     +  LASTS
    |            |           |            |              
3y(8y²-2y) + (3y)(-9) + (11)(8y²-2y) + (11)(-9)

(24y³-6y²) +  (-27y)  +  (88y²-22y)  +  (-99)

   24y³ - 6y² - 27y + 88y² - 22y - 99

Combining like terms and arranging terms in descending order:

    24y³ + 82y² - 49y - 99 

That answer is correct even though you don't have it listed.  My guess
is that it is (C) and you inadvertently reversed the digits of 82 as 28.

Edwin
AnlytcPhil@aol.com
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