factorise by spletting middle term, 6x2+x-2
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1
Answer:
Let's use the AC Method.
First multiply the coefficient (
A
=
6
) of the
x
2
term by the coefficient (
C
=
2
) of the constant term - ignoring the sign.
A
C
=
6
⋅
2
=
12
Notice that the sign of the constant (
C
) term is negative.
According to the AC Method, we need to look for a factorisation of our
A
C
value into a pair of factors, whose difference is the middle coefficient
B
=
1
. Well
4
×
3
=
12
and
4
−
3
=
1
. So the pair we want is
4
and
3
.
Now use this pair to split the middle term then factor by grouping:
6
x
2
−
x
−
2
=
6
x
2
−
4
x
+
3
x
−
2
=
(
6
x
2
−
4
x
)
+
(
3
x
−
2
)
=
2
x
(
3
x
−
2
)
+
(
3
x
−
2
)
=
(
2
x
−
1
)
(
3
x
−
2
)
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