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If \(x+2\) is a factor of the polynomial \(p(x)=x^3+mx^2-4x-4\), what is the value of \(m\)?
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Answer and explanation
Correct answer: 1
By the factor theorem, if \(x+2\) is a factor, then \(p(-2)=0\). Therefore, \((-2)^3+m(-2)^2-4(-2)-4=0\), which gives \(-8+4m+8-4=0\). Hence \(4m-4=0\), so \(m=1\). Exam tip: for a factor \(x-a\), substitute \(x=a\); thus, for \(x+2=x-(-2)\), substitute \(x=-2\).
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
By the factor theorem, if \(x+2\) is a factor, then \(p(-2)=0\). Therefore, \((-2)^3+m(-2)^2-4(-2)-4=0\), which gives \(-8+4m+8-4=0\). Hence \(4m-4=0\), so \(m=1\). Exam tip: for a factor \(x-a\), substitute \(x=a\); thus, for \(x+2=x-(-2)\), substitute \(x=-2\).
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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