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If \(p(x)=5x^3-2x^2+x-4\), what is the sum of all the coefficients of \(p(x)\)?
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Answer and explanation
Correct answer: 0
The sum of all coefficients of a polynomial is found by evaluating it at \(x=1\). Here, \(p(1)=5(1)^3-2(1)^2+1-4=5-2+1-4=0\). Therefore, the correct answer is 0. Exam tip: use \(p(1)\) for the sum of coefficients, not \(p(0)\), which gives only the constant term.
Frequently asked questions
What is the correct answer to this question?
0
Why is this the correct answer?
The sum of all coefficients of a polynomial is found by evaluating it at \(x=1\). Here, \(p(1)=5(1)^3-2(1)^2+1-4=5-2+1-4=0\). Therefore, the correct answer is 0. Exam tip: use \(p(1)\) for the sum of coefficients, not \(p(0)\), which gives only the constant term.
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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