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Trigonometry Examples
Popular Problems Trigonometry Factor f(x)=x^4-10x^3+35x^2-50x+24
f
(
x
)
=
x
4
−
10
x
3
+
35
x
2
−
50
x
+
24
Factor
x
4
−
10
x
3
+
35
x
2
−
50
x
+
24
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
,
±
24
,
±
2
,
±
12
,
±
3
,
±
8
,
±
4
,
±
6
q
=
±
1
Find every combination of
±
p
q
. These are the possible roots of the polynomial function.
±
1
,
±
24
,
±
2
,
±
12
,
±
3
,
±
8
,
±
4
,
±
6
Substitute
1
and simplify the expression. In this case, the expression is equal to
0
so
1
is a root of the polynomial.
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Substitute
1
into the polynomial.
1
4
−
10
⋅
1
3
+
35
⋅
1
2
−
50
⋅
1
+
24
Raise
1
to the power of
4
.
1
−
10
⋅
1
3
+
35
⋅
1
2
−
50
⋅
1
+
24
Raise
1
to the power of
3
.
1
−
10
⋅
1
+
35
⋅
1
2
−
50
⋅
1
+
24
Multiply
−
10
by
1
.
1
−
10
+
35
⋅
1
2
−
50
⋅
1
+
24
Subtract
10
from
1
.
−
9
+
35
⋅
1
2
−
50
⋅
1
+
24
Raise
1
to the power of
2
.
−
9
+
35
⋅
1
−
50
⋅
1
+
24
Multiply
35
by
1
.
−
9
+
35
−
50
⋅
1
+
24
Add
−
9
and
35
.
26
−
50
⋅
1
+
24
Multiply
−
50
by
1
.
26
−
50
+
24
Subtract
50
from
26
.
−
24
+
24
Add
−
24 and 24=0
