If \(x=1\) is a zero of \(p(x)=x^3+x^2-10x+8\), what is the remaining quadratic factor?
Answer and explanation
Correct answer: \(x^2+2x-8\)
Since \(x=1\) is a zero, \((x-1)\) must be a factor of \(p(x)\). Dividing \(x^3+x^2-10x+8\) by \((x-1)\) gives the quotient \(x^2+2x-8\) with remainder \(0\). Verification: \((x-1)(x^2+2x-8)=x^3+x^2-10x+8\). Therefore, option A is correct. Exam tip: if \(a\) is a zero, divide the polynomial by \((x-a)\) to obtain the remaining factor.
Frequently asked questions
What is the correct answer to this question?
\(x^2+2x-8\)
Why is this the correct answer?
Since \(x=1\) is a zero, \((x-1)\) must be a factor of \(p(x)\). Dividing \(x^3+x^2-10x+8\) by \((x-1)\) gives the quotient \(x^2+2x-8\) with remainder \(0\). Verification: \((x-1)(x^2+2x-8)=x^3+x^2-10x+8\). Therefore, option A is correct. Exam tip: if \(a\) is a zero, divide the polynomial by \((x-a)\) to obtain the remaining factor.
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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