What type of polynomial is 9x + 1?
Answer and explanation
Correct answer: Linear
The degree of a non-zero polynomial is the greatest exponent of the variable having a non-zero coefficient. In 9x + 1, the term 9x has exponent 1, while the constant term 1 has exponent 0. Therefore, the greatest exponent is 1, so the polynomial has degree 1 and is called a linear polynomial. It is not constant because the expression changes when x changes. It is not quadratic or cubic because it contains no non-zero x² or x³ term. The coefficient 9 affects the slope or scale of the expression, but it does not change the classification; the degree alone determines whether this polynomial is linear.
Frequently asked questions
What is the correct answer to this question?
Linear
Why is this the correct answer?
The degree of a non-zero polynomial is the greatest exponent of the variable having a non-zero coefficient. In 9x + 1, the term 9x has exponent 1, while the constant term 1 has exponent 0. Therefore, the greatest exponent is 1, so the polynomial has degree 1 and is called a linear polynomial. It is not constant because the expression changes when x changes. It is not quadratic or cubic because it contains no non-zero x² or x³ term. The coefficient 9 affects the slope or scale of the expression, but it does not change the classification; the degree alone determines whether this polynomial is linear.
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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