x³+x²-14x-24 factorize
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We start from the given 3rd degree polynomial
x
3
+
x
2
−
14
x
−
24
Use the monomial
−
14
x
It is equal to
−
4
x
−
10
x
x
3
+
x
2
−
4
x
−
10
x
−
24
Rearrange
x
3
−
4
x
+
x
2
−
10
x
−
24
Regroup
(
x
3
−
4
x
)
+
(
x
2
−
10
x
−
24
)
Factoring
x
(
x
2
−
4
)
+
(
x
+
2
)
(
x
−
12
)
x
(
x
+
2
)
(
x
−
2
)
+
(
x
+
2
)
(
x
−
12
)
Factor out the common binomial factor
(
x
+
2
)
(
x
+
2
)
[
x
(
x
−
2
)
+
(
x
−
12
)
]
Simplify the expression inside the grouping symbol [ ]
(
x
+
2
)
[
x
2
−
2
x
+
x
−
12
]
(
x
+
2
)
(
x
2
−
x
−
12
)
Factoring the trinomial
x
2
−
x
−
12
=
(
x
+
3
)
(
x
−
4
)
We now have the factors
(
x
+
2
)
(
x
+
3
)
(
x
−
4
)
Final answer
x
3
+
x
2
−
14
x
−
24
=
(
x
+
2
)
(
x
+
3
)
(
x
−
4
)
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