Question

Tamara and Clyde got different answers when dividing 2x4 + 7x3 – 18x2 + 11x – 2 by 2x2 – 3x + 1. Analyze their individual work. Which statement about their answers is true?

Answer 1

(B) Clyde’s work is correct because Tamara did not subtract the terms correctly.

Answer 2

The statements and their individual answers are not provided in the question. However, please check the explanation given below for the equation.

Explanation:

• The equation given is
  `(2x^(4) + 7x^(3) + 18x^(2) + 11x -2)/(2x^(2) - 3x + 1 )`

• Divide the leading term of the dividend by the leading term of the divisor:
  `(2x^(4) )/(2x^(2) ) = x^(2)`

• Multiply it by the divisor:
  `x^(2) ({2x^(2) -3x +1) = 2x^(4) - 3x^(3) + x^(2)`

• Subtract the dividend from the obtained result:
  `(2x^(4) + 7x^(3) + 18x^(2) + 11x - 2) - (2x^(4) - 3x^(3) + x^(2) ) = (10x^(3) + 17x^(2) + 11x -2)`

• Divide the leading term of the obtained remainder by the leading term of the divisor:
  `(10x^(3))/(2x^(2) ) = 5x`

• Multiply it by the divisor:
  `5x (2x^(2) - 3x + 1) = 10x^(3) - 15x^(2) + 5x`

• Subtract the remainder from the obtained result:
  `(10x^(3) + 17x^(2) + 11x -2) - (10x^(3) - 15x^(2) + 5x) = (32x^(2) + 6x - 2)`

• Divide the leading term of the obtained remainder by the leading term of the divisor:
  `(32x^(2) )/(2x^(2) ) = 16`

• Multiply it by the divisor:
  `16 (2x^(2) - 3x +1) = 32x^(2) - 48x +16`

• Subtract the remainder from the obtained result:
  `(32x^(2) + 6x - 2) - (32x^(2) - 48x +16) = 54x - 18`

• Since the degree of the remainder is less than the degree of the divisor, then we are done.

• Therefore,
  `(2x^(4) + 7x^(3) + 18x^(2) + 11x -2)/(2x^(2) - 3x + 1 ) = (x^(2) + 5x +16 + (54x - 18)/(2x^(2) - 3x +1))`