How do you find the quotient of #(3x^2 + 4xy + 3xy + 4y^2) ÷ (x + y)#?

Answer 1

The remainder is #=0# and the quotient is #color(red)(=3x+4y#

# color(white)(aaaaaaa)##color(red)(3x+4y# #color(white)(aaaaaa)##-----# #color(white)(aaaaa)##|##3x^2+7xy +4y^2# #color(white)(aaaaaaaaaaaa)##3x^2+3xy# #color(white)(aaaaaaaaaaaaa)##0+4xy+4y^2# #color(white)(aaaaaaaaaaaaaaaa)##4xy+4y^2# #color(white)(aaaaaaaaaaaaaaaaa)##---# #color(white)(aaaaaaaaaaaaaaaaaaa)##0+0#
The remainder is #=0# and the quotient is #color(red)(=3x+4y#
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Answer 2

#" The Quotient="(3x+4y).#

#ul(3x^2+4xy)+ul(3xy+4y^2),#
#=x(3x+4y)+y(3x+4y),#
#=(3x+4y)(x+y).#
#:. (3x^2+4xy+3xy+4y^2) -: (x+y),#
#=(3x^2+4xy+3xy+4y^2)/(x+y),#
#={(3x+4y)(cancel(x+y))}/(cancel(x+y)),#
#=(3x+4y)," is the desired quotient."#

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Answer 3

To find the quotient of (3x^2 + 4xy + 3xy + 4y^2) ÷ (x + y), we can use polynomial long division or synthetic division.

Using polynomial long division:

  1. Divide the first term of the dividend (3x^2) by the first term of the divisor (x). The result is 3x.
  2. Multiply the divisor (x + y) by the quotient obtained in step 1 (3x), and subtract the result from the dividend (3x^2 + 4xy + 3xy + 4y^2 - 3x(x + y)).
  3. Bring down the next term of the dividend (-3xy).
  4. Repeat steps 1-3 until all terms have been divided.
  5. The quotient is the sum of the quotients obtained in each step. In this case, the quotient is 3x - 3y.

Using synthetic division:

  1. Set up the synthetic division table with the divisor (x + y) as the divisor and write the coefficients of the dividend (3, 4, 3, 4) in descending order.
  2. Bring down the first coefficient (3) to the bottom row.
  3. Multiply the divisor (x + y) by the result obtained in step 2 (3), and write the product below the next coefficient (4).
  4. Add the two numbers in the bottom row (3 + 4 = 7), and write the sum below the next coefficient (3).
  5. Repeat steps 3-4 until all coefficients have been divided.
  6. The quotient is the set of numbers in the bottom row, which in this case is 3, 7, and -3.

Therefore, the quotient of (3x^2 + 4xy + 3xy + 4y^2) ÷ (x + y) is 3x - 3y.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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