factorise 2x^3 - x² -15x+8
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2
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Answered by
3
Answer:
The solution is:
(
3
x
+
4
)
(
x
−
2
)
The polynomial is of the type
a
x
2
+
b
x
+
c
.
There are two ways to factor.
The first one:
we have to find two numbers whose sum is
−
2
(that is
c
) and whose product is
−
24
(that is
a
⋅
c
).
−
24
=
−
1
⋅
24
−
24
=
−
24
⋅
1
−
24
=
−
2
⋅
12
−
24
=
−
12
⋅
2
−
24
=
−
3
⋅
8
−
24
=
−
8
⋅
3
−
24
=
−
4
⋅
6
−
24
=
−
6
⋅
4
The couple of numbers whose sum is
−
2
is
−
6
,
4
.
Now we have to "split" the monomial
−
2
x
in two parts:
−
2
x
=
−
6
x
+
4
x
.
So our polynomial becomes:
3
x
2
−
6
x
+
4
x
−
8
=
3
x
(
x
−
2
)
+
4
(
x
−
2
)
=
(
x
−
2
)
(
3
x
+
4
)
.
If it is known the way to solve an equation of 2° degree, here there is the second way to factor it:
We can imagine that this polynomial "becomes" an equation:
3
x
2
−
2
x
−
8
=
0
, we can calculate the quantity
Δ
=
b
2
−
4
a
c
=
4
+
96
=
100
,
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