Question

Factorise: x^3-x^2+x-1​

Answer 1

Answer:

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Answer 2

Answer:

How can I factorize x3−x2−x+1 ?

One of the methods of factorization is using FACTOR & REMAINDER THEOREM:

Factor theorem states that (x-a) is a factor of p(x) if p(a) =0

& remainder theorem states that p(a) = 0 if (x-a) is a factor of p(x)

Given P(x) = x^3 - x² - x + 1

This is a cubic polynomial.. ie, its degree is 3.

So it contains 3 linear factors, the constant term of which will be the factors of the constant term of the polynomial. As while multiplying the constant terms of all 3 linear factors, the product should be +1

So we have +1 or -1 as the constant terms of 3 linear factors.

And as per factor & remainder theorem, (x-a) will be a factor of p(x), if p(a) =0

Here, p(x)= x^3-x²-x+1

& p(1) = 1^3–1²-1+1 = 0

So, ( x-1) is a factor of p(x)

Now if we divide p(x) by (x-1) we get a quadratic polynomial as its quotient. & remainder has to be 0. As (x-1) is a factor of it.

P(x) ÷(x-1) then quotient = (x²-1) which is further factorized into (x+1)& (x-1)

So all 3 factors of p(x) = (x-1)(x+1)(x-1)

Step-by-step explanation:

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