Download Infinite Algebra 2

Algebra 2
Name___________________________________ ID: 1
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Assignment
Date________________ Period____
State the possible rational zeros for each function. Then factor each and find all rational zeros.
1) f ( x) = 2 x 3 - 3 x 2 - 3 x + 2
2) f ( x) = 2 x 3 - 6 x 2 - 45 x - 27
3) f ( x) = 2 x 3 - 5 x 2 + 4 x - 1
4) f ( x) = 3 x 3 - 25 x 2 - 44 x + 10
Worksheet by Kuta Software LLC
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5) f ( x) = 2 x 3 + x 2 - 2 x - 1
6) f ( x) = 5 x 3 + 31 x 2 + 31 x + 5
7) f ( x) = 2 x 3 - 9 x 2 + x + 18
8) f ( x) = 5 x 3 - 31 x 2 + 31 x - 5
Worksheet by Kuta Software LLC
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9) f ( x) = x 3 + 11 x 2 + 13 x - 10
10) f ( x) = 2 x 3 + 14 x 2 + 21 x - 9
11) f ( x) = 4 x 4 + 4 x 3 - x 2 - x
12) f ( x) = x 4 + 6 x 3 - 7 x 2 - 18 x
Worksheet by Kuta Software LLC
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Answers to Assignment (ID: 1)
1) Possible rational zeros: ± 1, ± 2, ±
2) Possible rational zeros:
1
2
Factors to: f ( x) = (2 x - 1)( x - 2)( x + 1)
{ }
1
Rational zeros: , 2, -1
2
3) Possible rational zeros: ± 1, ±
1
2
1 3 9 27
± 1, ± 3, ± 9, ± 27, ± , ± , ± , ±
2 2 2
2
Factors to: f ( x) = ( x + 3)(2 x 2 - 12 x - 9)
Rational zeros: {-3}
4) Possible rational zeros:
1 2 5 10
± 1, ± 2, ± 5, ± 10, ± , ± , ± , ±
3 3 3
3
Factors to: f ( x) = ( x - 1) 2(2 x - 1)
{
1
Rational zeros: 1 mult. 2,
2
Factors to: f ( x) = (3 x + 5)( x 2 - 10 x + 2)
}
5) Possible rational zeros: ± 1, ±
{ }
Rational zeros: 1
2
6) Possible rational zeros: ± 1, ± 5, ±
Factors to: f ( x) = (2 x + 1)( x + 1)( x - 1)
{
1
2
Rational zeros: - , -1, 1
{
Factors to: f ( x) = ( x - 2)(2 x - 5 x - 9)
Rational zeros: {2}
9) Possible rational zeros: ± 1, ± 2, ± 5, ± 10
Factors to: f ( x) = ( x + 2)( x 2 + 9 x - 5)
Rational zeros: {-2}
1
2
1
4
Rational zeros:
{ }
1
, 1, 5
5
10) Possible rational zeros:
1 3 9
± 1, ± 3, ± 9, ± , ± , ±
2 2 2
Factors to: f ( x) = ( x + 3)(2 x 2 + 8 x - 3)
Rational zeros: {-3}
12) Possible rational zeros:
0, ± 1, ± 2, ± 3, ± 6, ± 9, ± 18
Factors to: f ( x) = x( x - 2)( x 2 + 8 x + 9)
Rational zeros: {0, 2}
Factors to: f ( x) = x( x + 1)(2 x + 1)(2 x - 1)
1 1
2 2
1
5
Factors to: f ( x) = (5 x - 1)( x - 1)( x - 5)
2
11) Possible rational zeros: 0, ± 1, ± , ±
}
8) Possible rational zeros: ± 1, ± 5, ±
1 3 9
± 1, ± 2, ± 3, ± 6, ± 9, ± 18, ± , ± , ±
2 2 2
{
1
5
Rational zeros: -5, - , -1
7) Possible rational zeros:
1
5
Factors to: f ( x) = ( x + 5)(5 x + 1)( x + 1)
}
Rational zeros: 0, -1, - ,
5
3
}
Worksheet by Kuta Software LLC
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