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Let’s check out your problem:
Factor.
\newline
10
v
2
+
40
v
−
50
10v^2 + 40v - 50
10
v
2
+
40
v
−
50
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Math Problems
Algebra 2
Factor quadratics
Full solution
Q.
Factor.
\newline
10
v
2
+
40
v
−
50
10v^2 + 40v - 50
10
v
2
+
40
v
−
50
Identify Common Factor:
First, look for a common factor in all terms.
10
v
2
+
40
v
−
50
10v^2 + 40v - 50
10
v
2
+
40
v
−
50
can be divided by
10
10
10
.
Divide by Common Factor:
Divide each term by
10
10
10
.
10
v
2
÷
10
=
v
2
10v^2 \div 10 = v^2
10
v
2
÷
10
=
v
2
,
40
v
÷
10
=
4
v
40v \div 10 = 4v
40
v
÷
10
=
4
v
,
−
50
÷
10
=
−
5
-50 \div 10 = -5
−
50
÷
10
=
−
5
. So,
10
v
2
+
40
v
−
50
=
10
(
v
2
+
4
v
−
5
)
10v^2 + 40v - 50 = 10(v^2 + 4v - 5)
10
v
2
+
40
v
−
50
=
10
(
v
2
+
4
v
−
5
)
.
Factor Quadratic Expression:
Now, factor the quadratic
v
2
+
4
v
−
5
v^2 + 4v - 5
v
2
+
4
v
−
5
. We need two numbers that multiply to
−
5
-5
−
5
and add to
4
4
4
.
Find Correct Numbers:
The numbers are
5
5
5
and
−
1
-1
−
1
because
5
×
−
1
=
−
5
5 \times -1 = -5
5
×
−
1
=
−
5
and
5
+
(
−
1
)
=
4
5 + (-1) = 4
5
+
(
−
1
)
=
4
.
Write Factored Form:
Write the factored form using these numbers.
\newline
v
2
+
4
v
−
5
=
(
v
+
5
)
(
v
−
1
)
v^2 + 4v - 5 = (v + 5)(v - 1)
v
2
+
4
v
−
5
=
(
v
+
5
)
(
v
−
1
)
.
Reintroduce Common Factor:
Now, put the common factor
10
10
10
back in.
\newline
10
(
v
2
+
4
v
−
5
)
=
10
(
v
+
5
)
(
v
−
1
)
10(v^2 + 4v - 5) = 10(v + 5)(v - 1)
10
(
v
2
+
4
v
−
5
)
=
10
(
v
+
5
)
(
v
−
1
)
.
More problems from Factor quadratics
Question
Factor out the greatest common factor. If the greatest common factor is
1
1
1
, just retype the polynomial.
\newline
4
x
3
−
6
x
2
4x^3 - 6x^2
4
x
3
−
6
x
2
\newline
______
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Posted 9 months ago
Question
Factor
x
4
+
8
x
2
+
16
x^4 + 8x^2 + 16
x
4
+
8
x
2
+
16
completely.
\newline
All factors in your answer should have integer coefficients.
\newline
______
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Posted 9 months ago
Question
Find the binomial that completes the factorization.
\newline
t
3
+
u
3
=
(
‾
)
(
t
2
−
t
u
+
u
2
)
t^3 + u^3 = (\underline{\hspace{1cm}}) (t^2 - tu + u^2)
t
3
+
u
3
=
(
)
(
t
2
−
t
u
+
u
2
)
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Posted 9 months ago
Question
Factor.
\newline
g
2
−
11
g
+
18
g^2 - 11g + 18
g
2
−
11
g
+
18
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Posted 9 months ago
Question
Factor.
\newline
2
y
3
−
y
2
+
16
y
−
8
2y^3 - y^2 + 16y - 8
2
y
3
−
y
2
+
16
y
−
8
\newline
______
\newline
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Posted 9 months ago
Question
Factor.
\newline
2
x
8
+
7
x
2
2x^8 + 7x^2
2
x
8
+
7
x
2
\newline
______
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Posted 10 months ago
Question
Factor.
\newline
9
y
12
+
4
y
5
−
y
2
9y^{12} + 4y^5 - y^2
9
y
12
+
4
y
5
−
y
2
\newline
______
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Posted 9 months ago
Question
Factor.
\newline
6
a
4
+
3
a
3
−
a
+
2
6a^4 + 3a^3 - a + 2
6
a
4
+
3
a
3
−
a
+
2
\newline
_____
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Posted 9 months ago
Question
Factor.
\newline
4
c
7
−
2
c
5
+
c
2
−
5
4c^7 - 2c^5 + c^2 - 5
4
c
7
−
2
c
5
+
c
2
−
5
\newline
_____
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Posted 9 months ago
Question
Factor.
\newline
7
m
9
+
2
m
6
−
m
3
+
4
m
−
10
7m^9 + 2m^6 - m^3 + 4m - 10
7
m
9
+
2
m
6
−
m
3
+
4
m
−
10
\newline
_____
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Posted 9 months ago
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