factorise it. x2-14x + 24.
Answers
Step-by-step explanation:
x²-14x+24
x²-12x-2x+24
x(x-12)-2(x-12)
(x-2)(X+12)
x=2,12
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Step-by-step explanation:
The rule to factorise any quadratic is to find two numbers such that
product
=
x
2
coefficient
×
constant coefficient
sum
=
x
coefficient
So for
x
2
+
14
x
+
24
we seek two numbers such that
product
=
1
⋅
24
=
24
sum
=
14
So if we looks at the factors of
24
and compute their sum we get (as all the terms re positive we only need to consider positive factors);
factor1
factor2
sum
24
1
25
12
2
14
6
4
10
3
8
11
So the factors we seek are
12
and
2
Therefore we can factorise the quadratic as follows:
x
2
+
14
x
+
24
=
x
2
+
12
x
+
2
x
+
24
∴
x
2
+
14
x
+
24
=
x
(
x
+
12
)
+
2
x
(
x
+
12
)
∴
x
2
+
14
x
+
24
=
(
x
+
2
)
(
x
+
12
)
This approach works for all quadratics (assuming it does factorise) , The middle step in the last section can usually be skipped with practice.