The degree of the polynomial 4x^2 - 3x^5 + 8x^6 is
2011
The degree of the polynomial 4x^2 - 3x^5 + 8x^6 is
- A.
6
- B.
5
- C.
3
- D.
2
Attempted by 3 students.
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Correct answer: A
Concept: The degree of a polynomial is defined as the highest exponent that appears on its variable among the terms whose coefficient is not zero. Every term of the form a·xn contributes the value n as a candidate for the degree, and the degree of the whole polynomial is the maximum of these candidate values.
The term 4x2 has exponent 2, and its coefficient 4 is nonzero, so 2 is a candidate.
The term -3x5 has exponent 5, and its coefficient -3 is nonzero, so 5 is a candidate.
The term 8x6 has exponent 6, and its coefficient 8 is nonzero, so 6 is a candidate.
Comparing the candidates 2, 5 and 6, the largest value is 6.
Cross-check: reordering the polynomial in standard descending form gives 8x6 - 3x5 + 4x2, and the leading (first) term in this standard form is the one with exponent 6 — confirming the same result independently.
So the degree of the polynomial is 6.