Question

If x^3+ bx+c has -1 as a root and leaves a reminder of -6 when is divided by x+2 ,what are b and c?

Answer 1

Answer : $(b,c)=(-1,0)$

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Before we solve the question

• These dots are important part

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For convenience, $f(x)=x^3+bx+c$

• To solve, use remainder theorem
• Make system equation

We are being given the remainder of x+2 and a root.

According to the remainder theorem, $f(-2)=-6$

• $f(-2)=-8-2b+c$

And since -1 is a root, $f(-1)=0$

• $f(-1)=-1-b+c$

Now solve $\left \{ {{-8-2b+c=-6} \atop {-1-b+c=0}} \right.$

• The solution is $(b,c)=(-1,0)$

And hence $f(x)=x^3-x$