Foundations of Math 3
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Unit 10 Worksheet 2
Date________________ Period____
State the possible, rational zeros for each function, find all zeros, state their multiplicity if applicable and write in factored form. 1) f ( x) = 5x 3 + 9x 2 + 3x - 1
2) f ( x) = 3x 3 - 7x 2 - 7x + 3
3) f ( x) = x 3 + 16x 2 + 61x + 30
4) f ( x) = 2x 3 - x 2 - 5x - 2
5) f ( x) = x 3 - 11x 2 + 34x - 20
6) f ( x) = x 3 - 3x 2 - 27x - 27
7) f ( x) = 2x 3 + 3x 2 - 24x + 20
8) f ( x) = 2x 3 + 19x 2 - 80x + 50
9) f ( x) = 2x 3 + x 2 - 14x + 3
10) f ( x) = 5x 3 - 31x 2 + 31x - 5
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11) f ( x) = 3x 3 + 16x 2 - 25x - 10
12) f ( x) = 5x 3 + 4x 2 - 21x + 4
13) f ( x) = 3x 3 + 5x 2 - 11x + 3
14) f ( x) = 3x 3 + 7x 2 + 5x + 1
15) f ( x) = 4x 3 + 9x 2 + 6x + 1
16) f ( x) = x 3 - x 2 - 26x + 30
17) f ( x) = 2x 3 + x 2 - 2x - 1
18) f ( x) = x 3 - 8x 2 + 19x - 20
19) f ( x) = 5x 3 - 23x 2 - 23x + 21
20) f ( x) = x 3 - 5x 2 - x + 5
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Answers to Unit 10 Worksheet 2 1) Possible rational zeros: ± 1, ±
1 5
2) Possible rational zeros: ± 1, ± 3, ±
Factors to: f ( x) = ( x - 3)(3x - 1)( x + 1) 1 Zeros: 3, , -1 3
2
Factors to: f ( x) = ( x + 1) (5x - 1) 1 Zeros: -1 mult. 2, 5 3) Possible rational zeros:
{
{
}
Factors to: f ( x) = ( x + 5)( x 2 + 11x + 6) -11 + 97 -11 - 97 Zeros: -5, , 2 2 5) Possible rational zeros:
{
}
± 1, ± 2, ± 4, ± 5, ± 10, ± 20
Factors to: f ( x) = ( x - 5)( x 2 - 6x + 4) Zeros: {5, 3 + 5, 3 - 5 } 7) Possible rational zeros: 1 5 ± 1, ± 2, ± 4, ± 5, ± 10, ± 20, ± , ± 2 2
{
}
1 2
9) Possible rational zeros: ± 1, ± 3, ± , ±
3 2
Factors to: f ( x) = ( x + 3)(2x 2 - 5x + 1) 5 + 17 5 - 17 Zeros: -3, , 4 4 11) Possible rational zeros:
}
1 2 5 10 ± 1, ± 2, ± 5, ± 10, ± , ± , ± , ± 3 3 3 3
{
}
1 3
Factors to: f ( x) = (3x - 1)( x - 1)( x + 3) 1 Zeros: , 1, -3 3
}
1 2
15) Possible rational zeros: ± 1, ± , ±
1 4
2
Factors to: f ( x) = ( x + 1) (4x + 1) 1 Zeros: -1 mult. 2, 4
{
}
17) Possible rational zeros: ± 1, ±
1 2
f ( x) = (2x + 1)( x - 1)( x + 1)
Factors to: 1 Zeros: - , 1, -1 2
{
}
Factors to: f ( x) = (2x + 1)( x + 1)( x - 2) 1 Zeros: - , -1, 2 2 6) Possible rational zeros: ± 1, ± 3, ± 9, ± 27 Factors to: f ( x) = ( x + 3)( x 2 - 6x - 9) Zeros: {-3, 3 + 3 2, 3 - 3 2 }
{
}
8) Possible rational zeros: Factors to: f ( x) = (2x - 5)( x 2 + 12x - 10) 5 Zeros: , -6 + 46, -6 - 46 2
{
}
10) Possible rational zeros: ± 1, ± 5, ±
1 5
Factors to: f ( x) = (5x - 1)( x - 5)( x - 1) 1 Zeros: , 5, 1 5 12) Possible rational zeros:
{ }
1 2 4 ± 1, ± 2, ± 4, ± , ± , ± 5 5 5
Factors to: f ( x) = (3x + 1)( x 2 + 5x - 10) 1 -5 + 65 -5 - 65 Zeros: - , , 3 2 2
{
1 2
1 5 25 ± 1, ± 2, ± 5, ± 10, ± 25, ± 50, ± , ± , ± 2 2 2
Factors to: f ( x) = ( x - 2)(2x 2 + 7x - 10) -7 + 129 -7 - 129 Zeros: 2, , 4 4
13) Possible rational zeros: ± 1, ± 3, ±
}
4) Possible rational zeros: ± 1, ± 2, ±
± 1, ± 2, ± 3, ± 5, ± 6, ± 10, ± 15, ± 30
{
1 3
Factors to: f ( x) = (5x - 1)( x 2 + x - 4) 1 -1 + 17 -1 - 17 Zeros: , , 5 2 2
{
}
14) Possible rational zeros: ± 1, ±
1 3
2
Factors to: f ( x) = ( x + 1) (3x + 1) 1 Zeros: -1 mult. 2, 3 16) Possible rational zeros:
{
}
± 1, ± 2, ± 3, ± 5, ± 6, ± 10, ± 15, ± 30
Factors to: f ( x) = ( x - 5)( x 2 + 4x - 6) Zeros: {5, -2 + 10, -2 - 10 } 18) Possible rational zeros: ± 1, ± 2, ± 4, ± 5, ± 10, ± 20
Factors to: f ( x) = ( x - 5)( x 2 - 3x + 4) 3+i 7 3-i 7 Zeros: 5, , 2 2
{
}
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19) Possible rational zeros: 1 3 7 21 ± 1, ± 3, ± 7, ± 21, ± , ± , ± , ± 5 5 5 5
Factors to: f ( x) = (5x - 3)( x 2 - 4x - 7) 3 Zeros: , 2 + 11, 2 - 11 5
{
20) Possible rational zeros: ± 1, ± 5 Factors to: f ( x) = ( x - 5)( x + 1)( x - 1) Zeros: {5, -1, 1}
}
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