Polynomials and Expressions

Simplifying

Simplify the expression

3 x^{2} - 2 x + 1 - (2 x^{2} - x + 2)

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Polynomial Division

Divide the polynomial

3 x^{3} - 2 x^{2} + 5 x - 7

by the polynomial

x - 2

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Finding the Remainder Using Long Polynomial Division

Find the remainder when

2 x^{3} - 3 x^{2} + 4 x - 5

is divided by

x - 2

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Reducing

Reduce the polynomial

3 x^{4} - 2 x^{3} + 4 x^{2} - 5 x + 2

by factoring out the greatest common factor.

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Cancelling the Common Factors

Simplify the expression

\frac{4 x^{3} y^{2} z^{4}}{2 x^{2} y^{2} z^{2}}

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Evaluate the Expression Using the Given Values

Evaluate the polynomial expression

2 x^{3} - 5 x^{2} + 3 x - 7

for

x = - 2

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Identifying Degree

What is the degree of the polynomial

3 x^{4} - 2 x^{3} + x^{2} - 5 x + 7

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Multiplying Polynomials Using FOIL

Multiply the following polynomials using FOIL:

(x + 3)

and

(x - 2)

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Negative Exponents

Simplify the expression

5 x^{- 2} y^{- 3}

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Operations on Polynomials

Given two polynomial expressions,

P (x) = 3 x^{3} - 2 x^{2} + 4 x - 1

and

Q (x) = 2 x^{3} + 3 x^{2} - 5 x + 2

. Compute the sum of

P (x)

and

Q (x)

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Simplifying Expressions

Simplify the expression

3 x^{2} - 2 x + 5 + 7 x^{2} - 3 x + 2

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Factoring Using Any Method

Factorize the polynomial

4 x^{2} - 16 x + 16

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Factoring a Difference of Squares

Factorize the given expression:

a^{4} - 16

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Factoring a Sum of Cubes

Factor the polynomial expression

x^{3} + 8

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Factoring Out Greatest Common Factor (GCF)

Factor out the Greatest Common Factor (GCF) from the polynomial

12 x^{3} y + 18 x^{2} y^{2} + 24 x^{4} y^{3}

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Trinomial Squares

Simplify the trinomial square

(x + 5)^{2}

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Factoring by Grouping

Factorize the expression

3 x^{3} + 3 x^{2} - 4 x - 4

by grouping.

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Factoring a Difference of Cubes

Factor the expression

64 x^{3} - 125

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Factoring Trinomials

Factorize the trinomial

2 x^{2} - 5 x - 3

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Maximum Number of Real Roots/Zeros

What is the maximum number of real zeros for the polynomial

f (x) = 7 x^{5} - 3 x^{4} + 9 x^{3} - 5 x^{2} + 2 x - 8

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Finding All Possible Roots/Zeros (RRT)

Find all possible roots for the polynomial

3 x^{3} - 2 x^{2} - 5 x + 10

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Finding All Roots with Rational Root Test (RRT)

Find all roots of the polynomial

2 x^{3} - 3 x^{2} - 23 x + 30

using the Rational Root Test (RRT).

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Simplifying

Polynomial Division

Finding the Remainder Using Long Polynomial Division

Reducing

Cancelling the Common Factors

Evaluate the Expression Using the Given Values

Identifying Degree

Multiplying Polynomials Using FOIL

Negative Exponents

Operations on Polynomials

Simplifying Expressions

Factoring Using Any Method

Factoring a Difference of Squares

Factoring a Sum of Cubes

Factoring Out Greatest Common Factor (GCF)

Trinomial Squares

Factoring by Grouping

Factoring a Difference of Cubes

Factoring Trinomials

Maximum Number of Real Roots/Zeros

Finding All Possible Roots/Zeros (RRT)

Finding All Roots with Rational Root Test (RRT)

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