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Question 174121: please give me the answers..
use a caret (^) to indicate the power. For example, 53 would be written as 5^3.
1. Write the equation of a polynomial that has zeros at –3 and 2.
Write each polynomial function in standard form. Then classify it by degree and by the number of terms.
2. n = 4m2 – m + 7m4
n = 4m3 + 4m – 2; cubic trinomial
n = 7m4 + 4m2 – m; quartic trinomial
n = 4m4 + 8m2 – m ; quartic trinomial
n = 3m3 + 2m – 5; cubic trinomial
3. f(t) = 4t + 3t3 + 2t – 7
f(t) = 3t3 + 6t – 7; cubic trinomial
f(t) = 2t3 + 4t – 1; cubic trinomial
f(t) = 5t3 + 2t – 7; cubic trinomial
f(t) = 7t3 + 3t – 4; cubic trinomial
4. f(r) = 5r + 7 + 2r2
f(r) = 8r3 + 5r + 1; cubic trinomial
f(r) = r2 + 5r + 7; quadratic trinomial
f(r) = 2r3 + 5r + 7; cubic trinomial
f(r) = 2r2 + 5r + 7; quadratic trinomial
For each function, determine the zeros and their multiplicity.
5. y = (x + 2)2(x – 5)4
–2, multiplicity 2; 5, multiplicity 4
2, multiplicity 2; 5, multiplicity 3
–2, multiplicity 4; 5, multiplicity 2
2, multiplicity 2; 7, multiplicity 4
6. y = (3x + 2)3(x – 5)5
4, multiplicity 2; 5, multiplicity 2
3, multiplicity 4; 2, multiplicity 4
, multiplicity 3; 5, multiplicity 5
2, multiplicity 3; 5, multiplicity 5
7. y = x2(x + 4)3(x – 1)
2, multiplicity 2; –4, multiplicity 2; 1, multiplicity 1
0, multiplicity 2; –4, multiplicity 3; 1, multiplicity 1
3, multiplicity 4; –3, multiplicity 2; 2, multiplicity 3
0, multiplicity 2; –3, multiplicity 2; 2, multiplicity 3
8. (x3 + 3x2 – x – 3) ÷ (x – 1)
10. Use synthetic division to find P(–3) for P(x) = –2x4 – 3x3 – x + 4.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1. Write the equation of a polynomial that has zeros at –3 and 2.
Equation: f(x) = (x+3)(x-2)
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Write each polynomial function in standard form. Then classify it by degree and by the number of terms.
2. n = 4m2 – m + 7m4
n = 4m3 + 4m – 2; cubic trinomial
n = 7m4 + 4m2 – m; quartic trinomial---Correct
n = 4m4 + 8m2 – m ; quartic trinomial
n = 3m3 + 2m – 5; cubic trinomial
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3. f(t) = 4t + 3t3 + 2t – 7
f(t) = 3t3 + 6t – 7; cubic trinomial-----Correct
f(t) = 2t3 + 4t – 1; cubic trinomial
f(t) = 5t3 + 2t – 7; cubic trinomial
f(t) = 7t3 + 3t – 4; cubic trinomial
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4. f(r) = 5r + 7 + 2r2
f(r) = 8r3 + 5r + 1; cubic trinomial
f(r) = r2 + 5r + 7; quadratic trinomial
f(r) = 2r3 + 5r + 7; cubic trinomial
f(r) = 2r2 + 5r + 7; quadratic trinomial----Correct
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For each function, determine the zeros and their multiplicity.
5. y = (x + 2)^2(x – 5)^4
–2, multiplicity 2; 5, multiplicity 4----Correct
2, multiplicity 2; 5, multiplicity 3
–2, multiplicity 4; 5, multiplicity 2
2, multiplicity 2; 7, multiplicity 4
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6. y = (3x + 2)^3(x – 5)^5
4, multiplicity 2; 5, multiplicity 2
3, multiplicity 4; 2, multiplicity 4
-2/3, multiplicity 3; 5, multiplicity 5----Correct
2, multiplicity 3; 5, multiplicity 5
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7. y = x^2(x + 4)^3(x – 1)
2, multiplicity 2; –4, multiplicity 2; 1, multiplicity 1
0, multiplicity 2; –4, multiplicity 3; 1, multiplicity 1----Correct
3, multiplicity 4; –3, multiplicity 2; 2, multiplicity 3
0, multiplicity 2; –3, multiplicity 2; 2, multiplicity 3
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8. (x^3 + 3x^2 – x – 3) ÷ (x – 1)
1)....1....3....-1....-3
.......1....4.....3....|..0
Quotient: x^2 + 4x + 3
Remainder: 0
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10. Use synthetic division to find P(–3) for P(x) = –2x^4 – 3x^3 – x + 4
-3)....-2....-3....-1....4
.........-2....3.....-8..|..28
Quotient: -2x^2 + 3x -8
Remainder: 28
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Cheers,
Stan H.
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