when the function g(x)=x³+bx²-5x+2 is divided by (x-1) it leaves the same remainder as when it is divided by (x+2). Find the value of b.
I ve tried this so many times and I get -2 as my answer but it says 2 in the back. Some one please help
when the function g(x)=x³+bx²-5x+2 is divided by (x-1) it leaves the same remainder as when it is divided by (x+2). Find the value of b.
0
$\begingroup$
functions
polynomials
2 Answers
2
Hint: The question is equivalent to
Find $b$ given that $g(1)=g(-2)$.
This follows from this general fact:
The remainder of a polynomial $f(x)$ divided by $x-a$ is $f(a)$.
So, we have to solve $$ 1+b-5+2=-8+4b+10+2 $$ for $b$. This gives $b=-2$, as you have found.
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0It appears the OP knows this since OP got the correct answer $b=-2$ whereas the book answer was incorrect. – 2017-02-07
1
Your answer is correct, the book is wrong.
\begin{eqnarray} x^3-2x^2-5x+2&=&(x-1)(x^2-x-6)-4\\ &=&(x+2)(x^2-4x+3)-4 \end{eqnarray}
with equal remainders of $-4$.
Whereas
\begin{eqnarray} x^3+2x^2-5x+2&=&(x-1)(x^2+3x-0)+0\\ &=&(x+2)(x^2+4x+3)+8 \end{eqnarray}
which have unequal remainders of $0$ and $8$.
So the correct answer is $b=-2$.
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0Does this answer your question? – 2017-02-07