After simplifying (x^4(x^2+3)-x^6+5x^3), what is the degree?
Answer and explanation
Correct answer: 4
First expand: \(x^4(x^2+3)=x^6+3x^4\). Thus, the expression becomes \(x^6+3x^4-x^6+5x^3=3x^4+5x^3\). The \(x^6\) terms cancel. The highest power of \(x\) in the remaining polynomial is 4, so its degree is 4. Although 3 is the power in one term, it is not the highest power. Exam tip: simplify and combine like terms before finding the degree of a polynomial.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
First expand: \(x^4(x^2+3)=x^6+3x^4\). Thus, the expression becomes \(x^6+3x^4-x^6+5x^3=3x^4+5x^3\). The \(x^6\) terms cancel. The highest power of \(x\) in the remaining polynomial is 4, so its degree is 4. Although 3 is the power in one term, it is not the highest power. Exam tip: simplify and combine like terms before finding the degree of a polynomial.
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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