Divide the polynomial 6x³ + 13x² + x − 2 by 2x + 1, and find the quotient and…
2019
Divide the polynomial 6x³ + 13x² + x − 2 by 2x + 1, and find the quotient and remainder:
- A.
Q = 3x² + 5x − 2, R = 1
- B.
Q = 3x² − 5x + 2, R = 0
- C.
Q = 3x² − 5x − 2, R = 0
- D.
Q = 3x² + 5x − 2, R = 0
Attempted by 15 students.
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Correct answer: D
Solution:
Divide the leading terms: 6x^3 ÷ 2x = 3x^2. Multiply the divisor: (2x + 1)·3x^2 = 6x^3 + 3x^2. Subtract to get 10x^2 + x.
Divide 10x^2 by 2x to get 5x. Multiply the divisor: (2x + 1)·5x = 10x^2 + 5x. Subtract to get −4x − 2.
Divide −4x by 2x to get −2. Multiply the divisor: (2x + 1)·(−2) = −4x − 2. Subtract to obtain remainder 0.
Therefore: Quotient = 3x^2 + 5x − 2, Remainder = 0
Quick check: multiply the divisor and quotient to recover the dividend, or evaluate the polynomial at x = −1/2 (the root of 2x + 1). f(−1/2) = 0 confirms the remainder is 0.
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