factorize the expression x2-25+150x
Answers
Answered by
1
Answer:
We want to look for two numbers. These numbers should have a product of
150
and a sum of
25
.
Lets examine all the possible factors of
150
:
Product
−−−−−−−
Sum
−−−−
150
=
1
×
150
==⇒
1
+
150
=
151
150
=
2
×
75
==⇒
2
+
75
=
77
150
=
3
×
50
==⇒
3
+
50
=
53
150
=
5
×
30
==⇒
5
+
30
=
35
150
=
10
×
15
==⇒
10
+
15
=
25
So, the pair of numbers we're looking for are
10
and
15
.
So, we see that
x
2
+
25
x
+
150
=
(
x
+
10
)
(
x
+
15
)
Check this by expanding it again:
(
x
+
10
)
(
x
+
15
)
=
x
(
x
+
15
)
+
10
(
x
+
15
)
(
x
+
10
)
(
x
+
15
)
=
(
x
2
+
15
x
)
+
(
10
x
+
150
)
(
x
+
10
)
(
x
+
15
)
=
x
2
+
25
x
+
150
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