factorise:×^2+ 7×+12
Answers
We are looking for factors of 12 which ADD (because of + 12) up to 7.
The signs will be the same (because of + 12), they are both negative (because of -7).
The factors which satisfy both conditions are
−
3
and
−
4
.
−
3
×
−
4
=
+
12
,
and
−
3
+
−
4
=
−
7
(
x
−
3
)
(
x
−
4
)
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Let's look at the possible combinations of factors of
12
subtract
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12
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add
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
↓
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↓
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↓
11
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.
.
1
×
12
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13
4
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2
×
6
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8
1
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3
×
4
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7
←
3
and
4
are the
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.
.
factors we need.
In order to factorise easily you have to know the multiplication tables well. Without that it is a long slog with lots of trial and error!
Learn the tables!
x²+7x+12
x²+4x+3x+12
x(x+4)+3(x+4)