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Byju's Answer
Standard IX
Mathematics
Polynomials
Factorize eac...
Question
Factorize each of the following quadratic polynomials by using the method of completing the square:
q2 − 10q + 21
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Solution
q
2
-
10
q
+
21
=
q
2
-
10
q
+
10
2
2
-
10
2
2
+
21
[
Adding
and
subtracting
10
2
2
,
that
is
,
5
2
]
=
q
2
-
2
×
q
×
5
+
5
2
-
5
2
+
21
=
(
q
-
5
)
2
-
4
[
Completing
the
square
]
=
(
q
-
5
)
2
-
2
2
=
[
(
q
-
5
)
-
2
]
[
(
q
-
5
)
+
2
]
=
(
q
-
5
-
2
)
(
q
-
5
+
2
)
=
(
q
-
7
)
(
q
-
3
)
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