How to factorize x^3−7x+6?

Flambergru

Flambergru

Answered question

2022-08-12

How do you factorize this polynomial:
x 3 7 x + 6

Answer & Explanation

wijnvatid

wijnvatid

Beginner2022-08-13Added 16 answers

The method below will not always work, but it is another way to arrive at the same answer for this cubic.
This is difficult because it is a cubic, but if you consider the quadratic x 2 7 x + 6, that factors nicely as ( x 1 ) ( x 6 ). So we rewrite our given cubic as
x 3 7 x + 6 = ( x 3 x 2 ) + ( x 2 7 x + 6 ) .
Factorising each bracket, we have
x 3 7 x + 6 = ( x 3 x 2 ) + ( x 2 7 x + 6 ) = x 2 ( x 1 ) + ( x 1 ) ( x 6 ) = ( x 1 ) ( x 2 + x 6 ) = ( x 1 ) ( x 2 ) ( x + 3 ) .

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