How many terms are there in q(x) = x^3 + 2x^2 − x + 4?
Answer and explanation
Correct answer: 4
The governing concept is that separate polynomial terms are identified by addition or subtraction signs, while each term includes its sign when necessary. In q(x) = x^3 + 2x^2 − x + 4, the four terms are x^3, 2x^2, −x, and 4. Therefore the polynomial contains 4 terms, making option C correct. The minus sign before x does not create an additional term; it belongs to the coefficient of the term −x. Likewise, the constant 4 is itself one term. Counting only the variable terms would give 3, which is why option B is incomplete. The expression has no hidden fifth term, because there are only three separating signs and four resulting parts.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The governing concept is that separate polynomial terms are identified by addition or subtraction signs, while each term includes its sign when necessary. In q(x) = x^3 + 2x^2 − x + 4, the four terms are x^3, 2x^2, −x, and 4. Therefore the polynomial contains 4 terms, making option C correct. The minus sign before x does not create an additional term; it belongs to the coefficient of the term −x. Likewise, the constant 4 is itself one term. Counting only the variable terms would give 3, which is why option B is incomplete. The expression has no hidden fifth term, because there are only three separating signs and four resulting parts.
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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