Question

How do you factor `21x^3 - 18x^2 + 7x - 6` by grouping?

Answer 1

Expression`=3x^2(7x-6)+1(7x-6)=(7x-6)(3x^2+1).`

Explanation:

Observe that `3x^2` can be taken out as common from the first two terms, 7, from the last two terms, only `1` can be taken out. Hence,

Expression`=3x^2(7x-6)+1(7x-6)=(7x-6)(3x^2+1).`

Answer 2

`(7x-6)(3x^2+1)`

Explanation:

Group the terms in 'pairs' as follows.

`[21x^3-18x^2]+[7x-6]`

now factorise each 'pair'.

`color(red)(3x^2)(7x-6)color(red)(+1)(7x-6)`

We now have a common factor of (7x -6) in each pair which we can take out.

`(7x-6)(color(red)(3x^2+1))`

`rArr21x^3-18x^2+7x-6=(7x-6)(3x^2+1)`