1.

Without actual division, prove that `2x^(4)-5x^(3)+2x^(2)-x+2` is divisible by `x^(2)-3x+2`.

Answer» We have, `x^(2)-3x+2=x^(2)-x-2x+2=x(x-1)-2(x-1)=(x-1)(x-2)`
Let `p(x)=2x^(4)-5x^(3)+2x^(2)-x+2`
Now, `p(1)=2(1)^(4)-5(1)^(3)+2(1)^(2)-1+2=2-5+2-1+2=0`
Therefore, (x-1) divides p(x),
and `p(2)=2(2)^(4)-5(2)^(3)+2(2)^(2)-2+2=32-40+8-2+2=0`
Therefore, (x-2) divides p(x).
So, `(x-1)(x-2)=x^(2)-3x+2` divides `2x^(4)-5x^(3)+2x^(2)-x+2`


Discussion

No Comment Found

Related InterviewSolutions