What is the coefficient of x in x^3 + 4x^2 - 5?
Answer and explanation
Correct answer: 0
The governing concept is identification of the coefficient of a specified power. The coefficient of x means the numerical factor multiplying x^1. In x^3 + 4x^2 − 5, the visible terms have powers 3, 2 and 0; there is no x^1 term. A missing term is understood to have coefficient zero, so the polynomial can be written as x^3 + 4x^2 + 0x − 5. Therefore the coefficient of x is 0, making option C correct. Option A is the coefficient of x^3, option B is the coefficient of x^2, and option D is the constant term. The absence of a written x-term does not mean its coefficient is 1; it means the coefficient is zero.
Frequently asked questions
What is the correct answer to this question?
0
Why is this the correct answer?
The governing concept is identification of the coefficient of a specified power. The coefficient of x means the numerical factor multiplying x^1. In x^3 + 4x^2 − 5, the visible terms have powers 3, 2 and 0; there is no x^1 term. A missing term is understood to have coefficient zero, so the polynomial can be written as x^3 + 4x^2 + 0x − 5. Therefore the coefficient of x is 0, making option C correct. Option A is the coefficient of x^3, option B is the coefficient of x^2, and option D is the constant term. The absence of a written x-term does not mean its coefficient is 1; it means the coefficient is zero.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Polynomials in one variable.
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