Answer:
[tex]\frac{x+7}{3}[/tex]
Step-by-step explanation:
For a polynomial of the form
a
x
2
+
b
x
+
c
, rewrite the middle term as a sum of two terms whose product is
a
⋅
c
=
5
⋅
−
2
=
−
10
and whose sum is
b
=
9
.
Tap for fewer steps...
Factor
9
out of
9
x
.
5
x
2
+
9
(
x
)
−
2
x
2
+
12
x
+
20
⋅
x
2
+
17
x
+
70
15
x
−
3
Rewrite
9
as
−
1
plus
10
5
x
2
+
(
−
1
+
10
)
x
−
2
x
2
+
12
x
+
20
⋅
x
2
+
17
x
+
70
15
x
−
3
Apply the distributive property.
5
x
2
−
1
x
+
10
x
−
2
x
2
+
12
x
+
20
⋅
x
2
+
17
x
+
70
15
x
−
3
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(
5
x
2
−
1
x
)
+
10
x
−
2
x
2
+
12
x
+
20
⋅
x
2
+
17
x
+
70
15
x
−
3
Factor out the greatest common factor (GCF) from each group.
x
(
5
x
−
1
)
+
2
(
5
x
−
1
)
x
2
+
12
x
+
20
⋅
x
2
+
17
x
+
70
15
x
−
3
Factor the polynomial by factoring out the greatest common factor,
5
x
−
1
.
(
5
x
−
1
)
(
x
+
2
)
x
2
+
12
x
+
20
⋅
x
2
+
17
x
+
70
15
x
−
3
Factor
x
2
+
12
x
+
20
using the AC method.
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Consider the form
x
2
+
b
x
+
c
. Find a pair of integers whose product is
c
and whose sum is
b
. In this case, whose product is
20
and whose sum is
12
.
2
,
10
Write the factored form using these integers.
(
5
x
−
1
)
(
x
+
2
)
(
x
+
2
)
(
x
+
10
)
⋅
x
2
+
17
x
+
70
15
x
−
3
Factor
x
2
+
17
x
+
70
using the AC method.
Tap for fewer steps...
Consider the form
x
2
+
b
x
+
c
. Find a pair of integers whose product is
c
and whose sum is
b
. In this case, whose product is
70
and whose sum is
17
.
7
,
10
Write the factored form using these integers.
(
5
x
−
1
)
(
x
+
2
)
(
x
+
2
)
(
x
+
10
)
⋅
(
x
+
7
)
(
x
+
10
)
15
x
−
3
Simplify terms.
Tap for fewer steps...
Factor
3
out of
15
x
−
3
.
Tap for fewer steps...
Factor
3
out of
15
x
.
(
5
x
−
1
)
(
x
+
2
)
(
x
+
2
)
(
x
+
10
)
⋅
(
x
+
7
)
(
x
+
10
)
3
(
5
x
)
−
3
Factor
3
out of
−
3
.
(
5
x
−
1
)
(
x
+
2
)
(
x
+
2
)
(
x
+
10
)
⋅
(
x
+
7
)
(
x
+
10
)
3
(
5
x
)
+
3
(
−
1
)
Factor
3
out of
3
(
5
x
)
+
3
(
−
1
)
.
(
5
x
−
1
)
(
x
+
2
)
(
x
+
2
)
(
x
+
10
)
⋅
(
x
+
7
)
(
x
+
10
)
3
(
5
x
−
1
)
Cancel the common factor of
5
x
−
1
.
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Factor
5
x
−
1
out of
3
(
5
x
−
1
)
.
(
5
x
−
1
)
(
x
+
2
)
(
x
+
2
)
(
x
+
10
)
⋅
(
x
+
7
)
(
x
+
10
)
(
5
x
−
1
)
⋅
3
Cancel the common factor.
(
5
x
−
1
)
(
x
+
2
)
(
x
+
2
)
(
x
+
10
)
⋅
(
x
+
7
)
(
x
+
10
)
(
5
x
−
1
)
⋅
3
Rewrite the expression.
x
+
2
(
x
+
2
)
(
x
+
10
)
⋅
(
x
+
7
)
(
x
+
10
)
3
Cancel the common factor of
x
+
10
.
Tap for fewer steps...
Factor
x
+
10
out of
(
x
+
2
)
(
x
+
10
)
.
x
+
2
(
x
+
10
)
(
x
+
2
)
⋅
(
x
+
7
)
(
x
+
10
)
3
Factor
x
+
10
out of
(
x
+
7
)
(
x
+
10
)
.
x
+
2
(
x
+
10
)
(
x
+
2
)
⋅
(
x
+
10
)
(
x
+
7
)
3
Cancel the common factor.
x
+
2
(
x
+
10
)
(
x
+
2
)
⋅
(
x
+
10
)
(
x
+
7
)
3
Rewrite the expression.
x
+
2
x
+
2
⋅
x
+
7
3
Multiply
x
+
2
x
+
2
and
x
+
7
3
.
(
x
+
2
)
(
x
+
7
)
(
x
+
2
)
⋅
3
Cancel the common factor of
x
+
2
.
Tap for fewer steps...
Cancel the common factor.
(
x
+
2
)
(
x
+
7
)
(
x
+
2
)
⋅
3
Rewrite the expression.
x
+
7
3
