The polynomial 2x^3 minus 3x^2 plus x minus 5 is divided by x minus 2. What is the remainder?
AA remainder of 6
BA remainder of -5
CA remainder of 1
DA remainder of -35
Answer & Solution
Correct answer: C. A remainder of 1
1. The remainder theorem avoids long division completely.
2. Set the divisor equal to zero to find the value to substitute, so x minus 2 gives x equal to 2.
3. Now substitute 2 into the polynomial, term by term.
4. Two cubed is 8, and 2 multiplied by 8 is 16.
5. Two squared is 4, and 3 multiplied by 4 is 12, which is subtracted.
6. The remaining terms give plus 2 and minus 5.
7. So the total is 16 minus 12 plus 2 minus 5, which equals 1, and the remainder is 1.
8. The answer 6 is the trap for dropping the constant term, the answer -5 substitutes 1 instead of 2, and the answer -35 substitutes -2 by reading the divisor as x plus 2.
_Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 5: Polynomials_
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