Algebra 1 EOC review 1

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. For example, 3x² - 2x + 1 is a polynomial.

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How do you subtract polynomials?

Back

To subtract polynomials, you subtract the coefficients of like terms. For example, (3x² - 3x + 2) - (x² - 2x + 1) = (3x² - x²) + (-3x + 2x) + (2 - 1) = 2x² - x + 1.

Front

What does it mean if an equation has infinitely many solutions?

Back

An equation has infinitely many solutions if the two sides of the equation are identical for all values of the variable. For example, 2x + 4 = 2x + 4.

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What is the solution to the equation 2x + 4 = 2x + 4?

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The solution is infinite because both sides of the equation are the same for any value of x.

Front

What does it mean if an equation has one solution?

Back

An equation has one solution if there is exactly one value of the variable that makes the equation true. For example, 5x + 4 = 2x + 4 has one solution.

Front

How do you determine the number of solutions for an equation?

Back

To determine the number of solutions, simplify the equation. If you end up with a true statement (like 0 = 0), it has infinitely many solutions. If you get a false statement (like 0 = 5), it has no solutions. If you get a specific value for the variable, it has one solution.

Front

What is the first step in solving the equation 2x - 3 = 5?

Back

The first step is to add 3 to both sides to isolate the term with the variable.

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form ax + b = c.

Front

What is the standard form of a linear equation?

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The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

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What are like terms?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x² and 5x² are like terms, while 3x² and 4x are not.