Factorize by grouping
key notes:
If a polynomial has four terms, you may be able to factor by grouping. Once the terms are in standard order, factor out the highest common factor (HCF) of the first two terms and the HCF of the second two terms. If the expressions in brackets match, you can factor by grouping:
ac+ad+bc+bd
a(c+d)+b(c+d)
(a+b)(c+d)
Learn with an example
Factor.
m3–m2+10m–10=—————-
Factor by grouping.
m3–m2+10m–10
m2(m–1)+10(m–1) Factor by grouping; the expressions in brackets should match
(m2+10)(m–1) Apply the distributive property
Factor.
2q3+3q2+12q+18=——————
Factor by grouping.
2q3+3q2+12q+18
q2(2q+3)+6(2q+3)Factor by grouping; the expressions in brackets should match
(q2+6)(2q+3)Apply the distributive property
Factor.
14v3+7v2+20v+10=———–
Factor by grouping.
14v3+7v2+20v+10
7v2(2v+1)+10(2v+1)Factor by grouping; the expressions in brackets should match
(7v2+10)(2v+1)Apply the distributive property
let’s practice!
