factorise 2x^3+3x^2-11x-6 using synthetic division
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Algebra Examples
Popular Problems Algebra Factor 2x^3+3x^2-11x-6
2
x
3
+
3
x
2
−
11
x
−
6
Factor
2
x
3
+
3
x
2
−
11
x
−
6
using the rational roots test.
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If a polynomial function has integer coefficients, then every rational zero will have the form
p
q
where
p
is a factor of the constant and
q
is a factor of the leading coefficient.
p
=
±
1
,
±
6
,
±
2
,
±
3
q
=
±
1
,
±
2
Find every combination of
±
p
q
. These are the possible roots of the polynomial function.
±
1
,
±
0.5
,
±
6
,
±
3
,
±
2
,
±
1.5
Substitute
−
0.5
and simplify the expression. In this case, the expression is equal to
0
so
−
0.5
is a root of the polynomial.
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Substitute
−
0.5
into the polynomial.
2
(
−
0.5
)
3
+
3
(
−
0.5
)
2
−
11
⋅
−
0.5
−
6
Raise
−
0.5
to the power of
3
.
2
⋅
−
0.125
+
3
(
−
0.5
)
2
−
11
⋅
−
0.5
−
6
Multiply
2
by
−
0.125
.
−
0.25
+
3
(
−
0.5
)
2
−
11
⋅
−
0.5
−
6
Raise
−
0.5
to the power of
2
.
−
0.25
+
3
⋅
0.25
−
11
⋅
−
0.5
−
6
Multiply
3
by
0.25
.
−
0.25
+
0.75
−
11
⋅
−
0.5
−
6
Add
−
0.25
and
0.75
.
0.5
−
11
⋅
−
0.5
−
6
Multiply
−
11
by
−
0.5
.
0.5
+
5.5
−
6
Add
0.5
and
5.5
.
6
−
6
Subtract
6
from
6
.
0
Since
−
0.5
is a known root, divide the polynomial by
2
x
+
1
to find the quotient polynomial. This polynomial can then be used to find the remaining roots.
2
x
3
+
3
x
2
−
11
x
−
6
2
x
+
1
Divide
2
x
3
+
3
x
2
−
11
x
−
6
by
2
x
+
1
.
x
2
+
x
−
6