If 2x^2 + 5x - 3 is written in descending powers, which is the leading term?
Answer and explanation
Correct answer: 2x^2
The governing concept is the leading term of a polynomial. When a polynomial is arranged in descending powers, the leading term is the complete term containing the highest power of the variable, including its coefficient and sign. In 2x^2 + 5x - 3, the powers are 2, 1, and 0, so the first and highest-power term is 2x^2. Therefore option A is correct. The expression is already written in descending-power order. The term 5x has lower power 1, and -3 is the constant term with power 0. Option D, x^2, gives only the variable part and omits the coefficient 2, so it is not the complete leading term.
Frequently asked questions
What is the correct answer to this question?
2x^2
Why is this the correct answer?
The governing concept is the leading term of a polynomial. When a polynomial is arranged in descending powers, the leading term is the complete term containing the highest power of the variable, including its coefficient and sign. In 2x^2 + 5x - 3, the powers are 2, 1, and 0, so the first and highest-power term is 2x^2. Therefore option A is correct. The expression is already written in descending-power order. The term 5x has lower power 1, and -3 is the constant term with power 0. Option D, x^2, gives only the variable part and omits the coefficient 2, so it is not the complete leading term.
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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