Question

Factorisation by regrouping

1. x³+x²+x+1

Answer 1

Given expression is
1 + x + x^2 + x^3

We group the first two terms and the last two terms.

1 (1 + x) + x^2 (1 + x)
(1 + x^2) * (1 + x)

So given expression has two factors.

We can also write as:

$1 + x + {x}^{2} + {x}^{3} \\ = (1 + x) \times (1 + {x}^{2}) \\ \\ = \frac{1 - {x}^{4} }{1 - x} . \\ we \: can \: write \: also \: like \: this. \\ of \: course \: it \: is \: a \: fraction \: but \: not \: factorization.$