CBSE BOARD X, asked by ghanashyamvinod1, 1 year ago

Check whether x^2+x+1 is a factor of x^3-6x^2+11x-6 ?

Answers

Answered by adarsh1453

because when dividing

it leaves remainder

but factors do not leave remainder

ghanashyamvinod1: So what will we do it's a worksheet question and I think there is no way in having a wrong in it.

adarsh1453: first you divide it

adarsh1453: it leaves remainder 17x+1

Answered by KINGAMAN

Let p(x)=x^3-6x^2+11x-6 & g(x) =x^2+x+1

First, If g(x) is an factor of p(x) then it will leave zero reaminder when divided by it .

So, After that we can follow long division method. As Per Solving it, Quoteint is x-7 and Remainder is 17x+1,Which is not equal to 0 And Thus,g(x) is not an factor of p(x)

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ghanashyamvinod1: That's the same I too got friend. But I have a problem and that is if it is a factor it's remainder needs to be zero but in this condition it isn't zero so how it can be a factor of p(x).

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