Factorize : x^2(x^2-14)+1
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Step-by-step explanation:
Explanation:
x
2
+
14
x
+
40
We can Split the Middle Term of this expression to factorise it.
In this technique, if we have to factorise an expression like
a
x
2
+
b
x
+
c
, we need to think of 2 numbers such that:
N
1
⋅
N
2
=
a
⋅
c
=
1
⋅
40
=
40
and,
N
1
+
N
2
=
b
=
14
After trying out a few numbers we get
N
1
=
10
and
N
2
=
4
10
⋅
4
=
40
, and
10
+
4
=
14
x
2
+
14
x
+
40
=
x
2
+
10
x
+
4
x
+
40
=
x
(
x
+
10
)
+
4
(
x
+
10
)
Here
(
x
+
10
)
is common to both terms.
So the factorised form is
=
(
x
+
4
)
(
x
+
10
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