Which option correctly explains why the product of (x + 3) and (2x − 1) is not linear?
Answer and explanation
Correct answer: Because its degree is 2
The governing concept is the degree of a polynomial and the effect of multiplication on degree. Expand the product: (x + 3)(2x − 1) = 2x² − x + 6x − 3 = 2x² + 5x − 3. The highest power of x is 2, and its coefficient is nonzero, so the product has degree 2. A linear polynomial must have degree 1; therefore this product is quadratic, not linear. Option B is correct. Option A describes a linear polynomial, while options C and D incorrectly claim that the result is constant or zero. The x² term cannot cancel, so the degree remains 2.
Frequently asked questions
What is the correct answer to this question?
Because its degree is 2
Why is this the correct answer?
The governing concept is the degree of a polynomial and the effect of multiplication on degree. Expand the product: (x + 3)(2x − 1) = 2x² − x + 6x − 3 = 2x² + 5x − 3. The highest power of x is 2, and its coefficient is nonzero, so the product has degree 2. A linear polynomial must have degree 1; therefore this product is quadratic, not linear. Option B is correct. Option A describes a linear polynomial, while options C and D incorrectly claim that the result is constant or zero. The x² term cannot cancel, so the degree remains 2.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Linear polynomials.
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