If (p(x)=(b-4)x^8+3x^3+2) and (b=4), what is the degree of (p(x))?
Answer and explanation
Correct answer: 3
On substituting \(b=4\), we get \(b-4=0\). Hence, the \(x^8\) term vanishes and the polynomial becomes \(3x^3+2\). The highest power of \(x\) now present is \(3\), so the degree is \(3\). Option 8 is incorrect because its coefficient becomes zero. Exam tip: Substitute any given parameter values first, then remove terms with zero coefficients before finding the degree.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
On substituting \(b=4\), we get \(b-4=0\). Hence, the \(x^8\) term vanishes and the polynomial becomes \(3x^3+2\). The highest power of \(x\) now present is \(3\), so the degree is \(3\). Option 8 is incorrect because its coefficient becomes zero. Exam tip: Substitute any given parameter values first, then remove terms with zero coefficients before finding the degree.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Degree of a Polynomial.
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