Tamara and Clyde got different answers when dividing 2 x to the 4th power plus 7 x cubed minus 18 x squared plus 11 x minus 2 by 2 x squared minus 3 x plus 1 Analyze their individual work. Tamara's Work Open image in full-screen view Clyde's Work Divisor Quotient x squared plus 5 x negative 2 2 x squared 2 x to the 4th power 10 x cubed negative 4 x squared negative 3 x negative 3 x cubed negative 15 x squared 6 x plus 1 x squared 5 x negative 2 negative 3 x cubed plus 10 x cubed is equal to 7 x cubed x squared plus open paren negative 15 x squared close paren plus open paren negative 4 x squared close paren is equal to negative 18 x squared 5 x plus 6 x is equal to 11 x Tamara's answer the fraction with numerator 2 x to the 4th power plus 7 x cubed minus 18 squared plus 11 x minus 2 and denominator 2 x squared minus 3 x plus 1 is equal to x squared plus 5 x minus 5 point 5 plus the fraction with numerator negative 7 point 5 x plus 3 point 5 and denominator 2 x squared minus 3 x plus 1 Clyde's answer the fraction with numerator 2 x to the 4th power plus 7 x cubed minus 18 squared plus 11 x minus 2 and denominator 2 x squared minus 3 x plus 1 is equal to x squared plus 5 x minus 2 Which statement about their answers is true?
Answer
A
Both students are incorrect.
B
Tamara’s work is correct because Clyde did not multiply the terms in the division table correctly.
C
Clyde’s work is correct because Tamara did not subtract the terms correctly.
D
Both students are correct.
Explanation
Dividing the leading terms gives 2x⁴ ÷ 2x² = x². Subtracting x²(2x² − 3x + 1) leaves 10x³ − 19x² + 11x − 2; then subtracting 5x(2x² − 3x + 1) leaves −4x² + 6x − 2. That is exactly −2(2x² − 3x + 1), so Clyde’s quotient, x² + 5x − 2, is correct. Tamara’s subtraction leads to an incorrect quotient and remainder.
AI-written and checked against the verified answer.

Question

Tamara and Clyde got different answers when dividing 2 x to the 4th power plus 7 x cubed minus 18 x squared plus 11 x minus 2 by 2 x squared minus 3 x plus 1 Analyze their individual work. Tamara's Work Open image in full-screen view Clyde's Work Divisor Quotient x squared plus 5 x negative 2 2 x squared 2 x to the 4th power 10 x cubed negative 4 x squared negative 3 x negative 3 x cubed negative 15 x squared 6 x plus 1 x squared 5 x negative 2 negative 3 x cubed plus 10 x cubed is equal to 7 x cubed x squared plus open paren negative 15 x squared close paren plus open paren negative 4 x squared close paren is equal to negative 18 x squared 5 x plus 6 x is equal to 11 x Tamara's answer the fraction with numerator 2 x to the 4th power plus 7 x cubed minus 18 squared plus 11 x minus 2 and denominator 2 x squared minus 3 x plus 1 is equal to x squared plus 5 x minus 5 point 5 plus the fraction with numerator negative 7 point 5 x plus 3 point 5 and denominator 2 x squared minus 3 x plus 1 Clyde's answer the fraction with numerator 2 x to the 4th power plus 7 x cubed minus 18 squared plus 11 x minus 2 and denominator 2 x squared minus 3 x plus 1 is equal to x squared plus 5 x minus 2 Which statement about their answers is true?

Answer

A

Both students are incorrect.

B

Tamara’s work is correct because Clyde did not multiply the terms in the division table correctly.

C

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

D

Both students are correct.

Explanation

Dividing the leading terms gives 2x⁴ ÷ 2x² = x². Subtracting x²(2x² − 3x + 1) leaves 10x³ − 19x² + 11x − 2; then subtracting 5x(2x² − 3x + 1) leaves −4x² + 6x − 2. That is exactly −2(2x² − 3x + 1), so Clyde’s quotient, x² + 5x − 2, is correct. Tamara’s subtraction leads to an incorrect quotient and remainder.

AI-written and checked against the verified answer.

Revolt · Accepted Answer

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

Polynomial Expressions — Test

Explanation

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