Factorise (x+1)(x+3)(x-4)(x-12)-24x^2
Answers
short,
x
3
+
x
2
−
24
x
+
36
would factor into
y
=
(
x
+
6
)
(
x
−
2
)
(
x
−
3
)
.
Explanation:
However, in order to get this you would need to use synthetic division.
First, start by finding all of the factors of 36:
±
1
,
±
2
,
±
3
,
±
6
,
±
9
,
±
12
,
±
18
,
and
±
36
.
Then, construct a sideways "L" (as is always the case in synthetic division).
Then, by trial and error, you would eventually find that
(
x
+
6
)
is one of the three factors of the polynomial, leaving you with
(
x
+
6
)
(
x
2
−
5
x
+
6
)
From here you would factor the
(
x
2
−
5
x
+
6
)
part into
(
x
−
2
)
(
x
−
3
)
. Then put everything together to get
(
x
+
6
)
(
x
−
2
)
(
x
−
3
)
Thus, the zeros of the polynomial are
x
=
−
6
,
x
=
2
,
x
=
3
P.S. To verify this, you can just expand the factored form, i.e.
the
(
x
+
6
)
(
x
−
2
)
(
x
−
3
)
, and you should get
x
3
+
x
2
−
24
x
+
36
as an answer. Hope this helps
Step-by-step explanation:
pls mark as brainliest answer
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