Exponents and Polynomials Review

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What is an exponent?

Back

An exponent is a number that shows how many times a base is multiplied by itself. For example, in 2^3, 2 is the base and 3 is the exponent, meaning 2 is multiplied by itself 3 times (2 * 2 * 2 = 8).

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What does it mean to simplify an expression with a negative exponent?

Back

A negative exponent indicates that the base should be taken as the reciprocal. For example, x^-2 = 1/x^2.

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What is a polynomial?

Back

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

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What is standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their exponents. For example, -5x^3 + 9x^2 + 2x is in standard form.

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How do you multiply two binomials?

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To multiply two binomials, use the distributive property (FOIL method): First, Outer, Inner, Last. For example, (x + 2)(x + 3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6.

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What is the result of (x^a)(x^b)?

Back

When multiplying like bases, add the exponents: (x^a)(x^b) = x^(a+b).

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What is the result of (x^a)/(x^b)?

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When dividing like bases, subtract the exponents: (x^a)/(x^b) = x^(a-b).

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What is the cube root of a number?

Back

The cube root of a number x is a value y such that y^3 = x. For example, the cube root of 27 is 3, since 3^3 = 27.

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What does it mean to simplify a radical expression?

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Simplifying a radical expression involves reducing it to its simplest form, which often means removing perfect squares or cubes from under the radical.

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What is the difference between a monomial and a polynomial?

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A monomial is a polynomial with only one term, such as 3x^2. A polynomial can have multiple terms, such as 2x^3 + 3x + 1.