Q. 4 Factorize x2 – 7x + 12
Answers
Step-by-step explanation:
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
)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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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...
↓
...
...
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...
...
...
...
↓
11
...
...
...
...
...
...
...
.
.
1
×
12
...
...
...
...
...
...
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
Answer:
x= 4 and 3
Step-by-step explanation:
x^2-3x-4x+12
x(x-3)-4(x-3)
(x-4)(x-3)
x-4=0, x-3=0
x=4, x=3.