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**Remainder & Factor Thms Finding Rational Roots**

More Thms Game page 100 100 100 200 200 200 300 300 300 400 400 400 500 500 500

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**Reminder and Factor Thrm. Finding Rational Roots**

Answer page Reminder and Factor Thrm. More Thrms. And Rules. Finding Rational Roots Is x+1 a factor of x15-3x-2 Yes Accord. To Descartes Rule, what is the possible # of positive roots of x3-2x2-5=0 1 Possible List the possible rational roots of 4x4+3x2-1=0 ± 1 , ± 2, ± 1/4 Find a poly. Whose roots are 0 and -1 d.r. X3+2x2+x Accord. To Descartes Rule, what is the possible # of negative roots of x3-2x2-5=0 0 Negative Solve over the real #’s x3-7x-6=0 (-1, -2, 3) Solve 2y3-5y2-4y+3 with root 3 3,-1,1/2 Find a cubric eq. w/ R coffs. That has the roots -1, 3-I X3-5x2+4x+10=0 Solve over the complex #’s 4x4-4x3+5x2-4x+1=0 1/2 (d.r.), ± i Solve x4-x3-2x-4=0 with root (±i, , -1, 2/3) Find the remaining roots of x4+x3+6x2-14x-20=0 -1 -3i ,-1 Solve over the Real #’s 2x3+x2-6x-3-x4+2x3-2x2+18=0 Solve 3x4-5x3-7x2+3x+2=0 (1± , -1, 2/3) Solve x4+12x-5=0 (1±2i, -1 ± Solve over the complex #’s 6x4+x3+23x2+4x-4=0 1/3, -1/2, ± 2i

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**Is x+1 a factor of x15 - 3x – 2 ? Correct Question**

Topic 1 – 100 / Answer

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C1-100 Q What is yes Topic / Question

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**Find a polynomial whose roots are 0 and -1 double root**

C Correct Question Topic 1 – 200 / Answer

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x3 + 2x2 + x C1-200 Q What is Topic / Question

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**Solve 2y3 – 5y2 – 4y + 3 with root 3 Correct Question**

Topic 1 – 300 / Answer

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C1-300 Q What is 3,-1, ½ Topic / Question

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**Solve x4 – x3 – 2x – 4 = 0 with root Correct Question**

Topic 1 – 400 / Answer

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C1-400 Q What are -1,2, Topic / Question

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**Solve 3x4–5x3–7x2+3x+2=0 given root Correct Question**

Topic 1 – 500 / Answer

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C1-500 Q What are , -1, 2/3 Topic / Question

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**According to Descartes’ Rule, what is the possible # of positive roots of**

x3-2x2-5=0 C Correct Question Topic 2 – 100 / Answer

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C2-100 Q What is 1 positive Topic / Question

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**According to Descartes’ Rule, what is the possible # of negative roots of**

x3-2x2-5=0 C Correct Question Topic 2 – 200 / Answer

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C2-200 Q What is 0 negative roots Topic / Question

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**Find a cubic equation with real coefficients that has the roots -1 and 3-i.**

Correct Question Topic 2 – 300 / Answer

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What is x3-5x2+4x+10=0 C2-300 Q Topic / Question

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**Find the remaining roots of**

x4+x3+6x2-14x-20= given its roots and -1+3i C Correct Question Topic 2 – 400 / Answer

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C2-400 Q What are -1-3i and -1 Topic / Question

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**Solve x4+12x-5=0 given 1-2i is a root.**

C Correct Question Topic 2 – 500 / Answer

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C2-500 Q What are Topic / Question

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**List the possible rational roots of 4x4 + 3x2 – 1 = 0**

C Correct Question Topic 3 – 100 / Answer

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C3-100 Q What is Topic / Question

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**Solve over the Real numbers:**

x3 – 7x – 6 = 0 C Correct Question Topic 3 – 200 / Answer

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What are -1,-2,3 C3-200Q Topic / Question

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**Solve over the complex numbers: 4x4-4x3+5x2-4x+1=0**

Correct Question Topic 3 – 300 / Answer

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What are ½ d.r., i,-i C3-300Q Topic / Question

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**Solve over the complex numbers: 2x3 + x2 - 6x – 3 =0 Correct Question**

Topic 3 – 400 / Answer

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What are -1/2, C3-400Q Topic / Question

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**Solve over the complex numbers:**

6x4+x3+23x2+4x-4=0 C Correct Question Topic 3 – 500 / Answer

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C3-500Q What is Topic / Question

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POD

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5.5 – Apply the Remainder and Factor Theorems The Remainder Theorem provides a quick way to find the remainder of a polynomial long division problem.

5.5 – Apply the Remainder and Factor Theorems The Remainder Theorem provides a quick way to find the remainder of a polynomial long division problem.

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