Algebra Concepts and Expressions

Algebra is a mathematical discipline that revolves around the utilization of symbols and the guidelines for manipulating these symbols. In algebra, expressions symbolize quantities and are made up of variables, numbers, and mathematical operations. These expressions lay the groundwork for equations and functions, which are crucial instruments in problem-solving and logical reasoning in mathematics.

Solving for a Variable

Let

f (x, y) = 2^{x} + 9 x y

, find

f (0, - 3), f (- 3, 2)

, and

f (3, 2)

f (0, - 3) = ◻

(Simplify your answer.)

f (- 3, 2) = ◻

(Simplify your answer.)

f (3, 2) = ◻

(Simplify your answer.)

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Polynomial Division

Find the remainder when the polynomial

f (x) = 3 x^{4} - 2 x^{3} + 4 x^{2} - 5 x + 1

is divided by the polynomial

g (x) = x^{2} - 3 x + 2

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Synthetic Division

Given the function

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

. Find the derivative of the function using synthetic division and algebraic concepts.

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Dividing

Let

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

. Find

f^{'} (2)

and then divide it by 2.

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Finding the Domain

Find the domain of the function

f (x) = \frac{1}{\sqrt{x^{2} - 9}}

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Finding the Range

Find the range of the function

f (x) = x^{2} + 5 x + 6

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Finding the Domain and Range

Find the domain and range of the function

f (x) = \sqrt{x^{2} - 9}

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Finding the Asymptotes

Find the vertical and horizontal asymptotes of the function

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

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Quadratic Inequalities

Solve the quadratic inequality

x^{2} - 3 x - 4 > 0

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Rational Inequalities

Solve the rational inequality

\frac{x^{2} - 4}{x^{2} - 5 x + 6} \geq 0

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Converting from Interval to Inequality

Find the interval notation of the solution set of the inequality

2 x^{2} - 5 x + 2 > 0

, then convert it into inequality notation.

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Finding the Holes in a Graph

Find the holes in the graph of the function

f (x) = \frac{x^{2} - 9}{x - 3}

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Algebra Concepts and Expressions

Solving for a Variable

Polynomial Division

Synthetic Division

Dividing

Finding the Domain

Finding the Range

Finding the Domain and Range

Finding the Asymptotes

Quadratic Inequalities

Rational Inequalities

Converting from Interval to Inequality

Finding the Holes in a Graph

Popular Problems