A monomial is a polynomial with only one term. For example, $$5x^3$$ and $$-2xy$$ are monomials.

A binomial is a polynomial with exactly two terms. For example, $$3x + 4$$ and $$x^2 - 5x$$ are binomials.

A trinomial is a polynomial with exactly three terms. For example, $$x^2 + 3x + 2$$ is a trinomial.

What does it mean to simplify an expression?

To simplify an expression means to combine like terms and reduce it to its simplest form. For example, $$2x + 3x - 5 = 5x - 5$$ .

What is the zero exponent rule?

The zero exponent rule states that any non-zero number raised to the power of zero equals one. For example, $$a^0 = 1$$ , where @@a eq 0@@.

What is the negative exponent rule?

The negative exponent rule states that a negative exponent indicates the reciprocal of the base raised to the opposite positive exponent. For example, $$a^{-n} = \frac{1}{a^n}$$ .

How do you multiply polynomials?

To multiply polynomials, use the distributive property (also known as the FOIL method for binomials) to multiply each term in one polynomial by each term in the other. For example, $$(x + 2)(x + 3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6$$ .

What is the difference between a polynomial and a rational expression?

A polynomial is an expression that consists of variables raised to non-negative integer powers, while a rational expression is a fraction where the numerator and/or denominator is a polynomial. For example, $$\frac{x^2 + 1}{x - 1}$$ is a rational expression.

What is the standard form of a polynomial?

The standard form of a polynomial is when the terms are arranged in descending order of their degrees. For example, $$4x^3 + 2x^2 - x + 5$$ is in standard form.

What is factoring in polynomials?

Factoring is the process of breaking down a polynomial into simpler components (factors) that, when multiplied together, give the original polynomial. For example, $$x^2 - 9 = (x - 3)(x + 3)$$ .

What is the significance of the leading coefficient?

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It influences the end behavior of the polynomial's graph.

Polynomials and Laws of Exponents Flashcards

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FLASHCARD QUESTION

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What is a polynomial?

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2.

FLASHCARD QUESTION

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What are the laws of exponents?

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