If \((x+1)\) is a factor of the polynomial \(2x^3+kx^2-5x+2\), what is the value of \(k\)?
Answer and explanation
Correct answer: -5
By the factor theorem, if \((x+1)\) is a factor, the polynomial must be zero at \(x=-1\). Thus, \(2(-1)^3+k(-1)^2-5(-1)+2=0\), giving \(-2+k+5+2=0\), so \(k+5=0\) and \(k=-5\). The value 5 is a close distractor caused by a sign error; remember that \(x+1=x-(-1)\), so substitute \(-1\), not 1.
Frequently asked questions
What is the correct answer to this question?
-5
Why is this the correct answer?
By the factor theorem, if \((x+1)\) is a factor, the polynomial must be zero at \(x=-1\). Thus, \(2(-1)^3+k(-1)^2-5(-1)+2=0\), giving \(-2+k+5+2=0\), so \(k+5=0\) and \(k=-5\). The value 5 is a close distractor caused by a sign error; remember that \(x+1=x-(-1)\), so substitute \(-1\), not 1.
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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