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Class 10 Mathematics Polynomials Polynomials in one variableHardLevel 46

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If (x+1) is a factor of the polynomial P(x)=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 of P(x), then P(-1)=0. Thus, P(-1)=2(-1)^3+k(-1)^2-5(-1)+2=-2+k+5+2=k+5. Hence, k+5=0, giving k=-5. Exam tip: for a factor of the form (x-a), substitute x=a; therefore, (x+1)=(x-(-1)) requires substituting x=-1.

Related tags

Polynomials Factor Theorem Polynomials In One Variable Linear Factor Parameter

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 of P(x), then P(-1)=0. Thus, P(-1)=2(-1)^3+k(-1)^2-5(-1)+2=-2+k+5+2=k+5. Hence, k+5=0, giving k=-5. Exam tip: for a factor of the form (x-a), substitute x=a; therefore, (x+1)=(x-(-1)) requires substituting x=-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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