How do you factor n^3+5n^2-4n-20 by grouping?
1 Answer
May 16, 2016
(n + 5)(n-2)(n+2)
Explanation:
'Group' the terms as follows:
[n^3+5n^2]+[-4n-20] now factorise each group.
rArrn^2(n+5)-4(n+5) There is now a common factor of (n +5) which can be taken out.
rArr(n+5)(n^2-4) now
n^2-4" is a difference of squares" which
color(blue)" In general is factorised as follows "
color(red)(|bar(ul(color(white)(a/a)color(black)(a^2-b^2=(a-b)(a+b))color(white)(a/a)|)))
rArrn^2-4=(n-2)(n+2)
rArrn^3+5n^2-4n-20=(n+5)(n-2)(n+2)
