Exam Review - Polynomials and Radical Equations

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What is a polynomial?

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A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to whole number powers and coefficients. For example, 5x^2 - 13x + 6 is a polynomial.

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What does it mean to factor a polynomial?

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Factoring a polynomial means expressing it as a product of its factors. For example, the polynomial 5x^2 - 13x + 6 can be factored into (5x - 3)(x - 2).

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What is a radical equation?

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How do you solve a radical equation?

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To solve a radical equation, isolate the radical on one side of the equation and then square both sides to eliminate the radical. Check for extraneous solutions afterward.

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What is the degree of a polynomial?

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The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 4x^3 + 2x^2 - x, the degree is 3.

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What is long division of polynomials?

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Long division of polynomials is a method used to divide a polynomial by another polynomial, similar to long division with numbers. It involves dividing, multiplying, and subtracting.

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What is the remainder theorem?

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The remainder theorem states that if a polynomial f(x) is divided by (x - c), the remainder of that division is f(c).

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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, while a polynomial can have multiple terms. For example, 3x is a monomial, while 3x + 2 is a polynomial.

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What is the zero product property?

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The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero. For example, if (x - 3)(x + 2) = 0, then x = 3 or x = -2.

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How do you factor the expression x^2 + 7x - 30?

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To factor x^2 + 7x - 30, look for two numbers that multiply to -30 and add to 7. The factors are (x + 10)(x - 3).