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

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

Step-by-step explanation:

• The equation given is $\frac{2x^{4} + 7x^{3} + 18x^{2} + 11x -2}{2x^{2} - 3x + 1 }$

• Divide the leading term of the dividend by the leading term of the divisor: $\frac{2x^{4} }{2x^{2} } = x^{2}$

•  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: $\frac{10x^{3}}{2x^{2} } = 5x$

• 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: $\frac{32x^{2} }{2x^{2} } = 16$

• 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,  $\frac{2x^{4} + 7x^{3} + 18x^{2} + 11x -2}{2x^{2} - 3x + 1 } = (x^{2} + 5x +16 + \frac{54x - 18}{2x^{2} - 3x +1})$

Answer 2

Answer:

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

Step-by-step explanation: