Polynomials (59 problems)

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Problem #1: Algebra - Polynomials - Complex Roots

Suppose that a polynomial function of degree 4 with rational coefficients has –1, 0, and 2 – 3i as zeros. What is the remaining zero?

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Problem #2: Algebra - Polynomials - Factoring a Polynomial

Factor the following polynomials:

,, ,, ,,

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Problem #3: Algebra - Polynomials - Operations of Polynomials

Divide using synthetic division:by.

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Problem #4: Algebra - Polynomials - Roots

Graph. Approximate to nearest tenth the real root of the equation

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Problem #5: Algebra~Polynomials~Operations of Polynomials~ID199

Find a rational function that hasandas vertical asymptotes, and (4,0) as an x-intercept.

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Problem #6: Algebra~Polynomials~Operations of Polynomials~ID200

Use synthetic division to find the quotient and remainder when

3x³ – x² + 4x – 10 is divided by x + 1.

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Problem #7: Algebra~Polynomials~Operations of Polynomials~ID201

Solve

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Problem #8: Algebra~Polynomials~Roots~ID160

Solve each

(a)

(b)

(c)

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Problem #9: Algebra~Polynomials~Roots~ID164

Solve

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Problem #10: Algebra~Polynomials~Roots~ID165

Solve

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Problem #11: Algebra~Polynomials~Roots~ID182

Consider the equation

(a) How many possible positive roots?

(b) How many possible negative roots?

(c) What are the possible rational roots?

(d) Using synthetic substitution, which of the possible roots is actually a root of the equation?

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Problem #12: Algebra~Polynomials~Roots~ID198

Find the zeros of the polynomial functionand state the multiplicity of each.

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Problem #13: Algebra~Polynomials~Simplification~ID158

Find (a) the GCF and (b) the LCM of the following monomials:

28, 35 and 42,

and

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Problem #14: Algebra~Polynomials~Simplification~ID161

Assuming that none of the terms is undefined, simplify each

(a)

(b)

(c)

(d)

(e)

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Problem #15: Algebra~Polynomials~Simplification~ID162

Simplify without negative exponents

(a)

(b)

(c)

(d)

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Problem #16: Algebra~Polynomials~Simplification~ID163

Simplify

(a)

(b)

(c)

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Problem #17: Algebra~Polynomials~~ID157

Expand

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Problem #18: Complex Roots

Express (7+3i)-(2-3i) in the form a + bi where a and b are real numbers.

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Problem #19: Factoring a Polynomial

Factor the polynomial: x - 5

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Problem #20: Factoring a Polynomial

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