Algebra Concepts and Expressions

Solving for a Variable

Use the binomial theorem to find the term containing

x^{- 33}

in the expansion

{(- 3 x + \frac{1}{x^{9}})}^{7}

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Solving by Graphing

Given the equations

y = 2 x + 3

and

y = - x + 1

, find the point of intersection by graphing.

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Polynomial Division

Divide the polynomial

3 x^{3} - 2 x^{2} + 5 x - 8

x - 2

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Finding the Remainder Using Long Polynomial Division

Find the remainder when

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

is divided by

x - 2

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Synthetic Division

Use synthetic division to divide

3 x^{3} - 2 x^{2} + 5 x - 8

x - 2

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Factoring Using Any Method

Factorize the following quadratic equation:

x^{2} - 5 x + 6 = 0

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Factoring a Difference of Squares

Factor the expression

25 x^{2} - 9

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Factoring a Sum of Cubes

Factor the expression

x^{3} + 8

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Factoring Out Greatest Common Factor (GCF)

Factorize the expression

15 x^{3} y^{2} - 10 x^{2} y - 5 x y

by factoring out the Greatest Common Factor (GCF).

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Factoring Trinomials

Factor the trinomial

x^{2} - 5 x + 6

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Partial Fraction Decomposition

Perform the partial fraction decomposition of the following rational function:

\frac{3 x^{2} - 2 x + 1}{x^{3} - x^{2}}

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Finding the Perfect Square Trinomial

Find the perfect square trinomial for the expression

x^{2} + 6 x

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Finding a Perpendicular Line Containing a Given Point

Find the equation of the line perpendicular to the line

3 x - 4 y = 12

and passes through the point

(2, - 1)

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Finding a Parallel Line Containing a Given Point

Find the equation of the line parallel to the line

4 x - 2 y = 6

and passing through the point

(1, 2)

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Reordering the Polynomial in Ascending Order

Reorder the polynomial

7 x^{3} - 5 x^{2} + 9 x - 4

in ascending order.

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Finding the LCM of a List of Expressions

Find the least common multiple (LCM) of the expressions

15 x^{2} y

5 x y^{2}

, and

30 x^{3} y^{2}

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Finding the LCD of a List of Expressions

Find the Least Common Denominator (LCD) of the list of expressions:

\frac{1}{x}, \frac{1}{x^{2}}, \frac{1}{x^{3}}

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Determining if the Number is a Perfect Square

Determine whether the number 324 is a perfect square. If so, what is its square root?

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Evaluate

Evaluate the expression

5 x^{2} - 3 x + 7

when

x = - 2

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Combining

Combine the expressions

3 x^{2} - 5 x + 7

and

4 x^{2} + 2 x - 3

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Finding the Domain

Find the domain of the function

f (x) = \sqrt{2 x + 3}

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Dividing

Divide the expression

\frac{6 x^{2} - 5 x - 1}{3 x + 2}

2 x - 1

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Evaluate the Expression Using the Given Values

Evaluate the expression

4 x^{2} - 3 y + z

for

x = 2

y = 1

, and

z = 3

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Evaluating the Difference Quotient

Evaluate the difference quotient for the function

f (x) = 3 x^{2} + 2 x + 1

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Evaluating Radicals

Simplify the expression

2 \sqrt{8} + 3 \sqrt{27}

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Determining if True

x = 2

and

y = 3

, is the equation

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

true?

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Finding the Holes in a Graph

Find the holes in the graph of the rational function

f (x) = \frac{x^{2} - 4}{x - 2}

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Solving for a Variable

Solving by Graphing

Polynomial Division

Finding the Remainder Using Long Polynomial Division

Synthetic Division

Factoring Using Any Method

Factoring a Difference of Squares

Factoring a Sum of Cubes

Factoring Out Greatest Common Factor (GCF)

Factoring Trinomials

Partial Fraction Decomposition

Finding the Perfect Square Trinomial

Finding a Perpendicular Line Containing a Given Point

Finding a Parallel Line Containing a Given Point

Reordering the Polynomial in Ascending Order

Finding the LCM of a List of Expressions

Finding the LCD of a List of Expressions

Determining if the Number is a Perfect Square

Evaluate

Combining

Finding the Domain

Dividing

Evaluate the Expression Using the Given Values

Evaluating the Difference Quotient

Evaluating Radicals

Determining if True

Finding the Holes in a Graph

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