Unit 4 Polynomials Review

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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, combined using addition, subtraction, and multiplication.

Front

What are the degrees of polynomials?

Back

The degree of a polynomial is the highest power of the variable in the expression. For example, in the polynomial 2x^3 + 3x^2 - x + 5, the degree is 3.

Front

What is the factored form of a polynomial?

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The factored form of a polynomial expresses it as a product of its factors, which can be linear or quadratic expressions. For example, (x-5)^2(x-2)(x+3) is a factored form.

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How do you find the zeros of a polynomial?

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To find the zeros of a polynomial, set the polynomial equal to zero and solve for the variable. The solutions are the x-values where the graph intersects the x-axis.

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What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation ax^2 + bx + c = 0 and is given by x = (-b ± √(b² - 4ac)) / (2a).

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What does it mean for a polynomial to be factored completely?

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A polynomial is factored completely when it is expressed as a product of irreducible polynomials over the given number system, meaning it cannot be factored further.

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What is synthetic division?

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Synthetic division is a simplified method of dividing a polynomial by a linear binomial of the form (x - c). It is faster than long division and is used to find polynomial quotients.

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What is the Remainder Theorem?

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

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What is the Factor Theorem?

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The Factor Theorem states that (x - c) is a factor of the polynomial f(x) if and only if f(c) = 0.

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How do you solve a quadratic equation by factoring?

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To solve a quadratic equation by factoring, express the equation in the form (x - p)(x - q) = 0, then set each factor equal to zero and solve for x.