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Polynomial Expressions — Test

Question 4 • Algebraic Reasoning

Amal used the tabular method to show her work dividing negative 2 x cubed plus 11 x squared minus 23 x plus 20 by x squared minus 3 x plus 4 Amal's Work Quotient 2 x plus 5 Divisor x squared negative 2 x cubed 5 x squared 6 x squared plus 5 x squared is equal to 11 x squared negative 3 x 6 x squared negative 15 x negative 8 x plus open paren negative 15 x close paren is equal to negative 23 x plus 4 negative 8 x 20 Amal's answer the fraction with numerator negative 2 x cubed plus 11 x squared minus 23 x plus 20 and denominator x squared minus 3 x plus 4 is equal to 2 x plus 5 Which statement about Amal’s work is true?

Answer
A
Amal’s work is incorrect because the like terms in the division table do not simplify to the original polynomial.
B
Amal’s work is correct.
C
Amal’s work is incorrect because it includes a positive two instead of negative two in the answer.
D
Amal’s work is incorrect because the wrong divisor is on the right side of the division table.

Explanation

Divide the leading terms: −2x³ ÷ x² = −2x, so the quotient must begin with −2x, not 2x. Multiplying −2x by the divisor gives −2x³ + 6x² − 8x; the remaining terms are 5x² − 15x + 20, which equal 5(x² − 3x + 4). Thus the quotient is −2x + 5, and Amal’s positive 2x makes her answer incorrect.

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