Math 3: EOC Review Unit 2 - Polynomial Functions

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What is a polynomial function?

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A polynomial function is a mathematical expression that involves a sum of powers in one or more variables multiplied by coefficients. The general form is f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where n is a non-negative integer and a_n ≠ 0.

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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 simpler polynomials or factors. This process helps in solving polynomial equations and simplifying expressions.

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What is the difference of cubes formula?

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The difference of cubes formula states that a^3 - b^3 = (a - b)(a^2 + ab + b^2).

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What is the sum of cubes formula?

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The sum of cubes formula states that a^3 + b^3 = (a + b)(a^2 - ab + b^2).

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How do you factor the expression 8x^3 - 1?

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8x^3 - 1 can be factored using the difference of cubes formula: (2x - 1)(4x^2 + 2x + 1).

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What is the quadratic formula?

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

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How do you factor the expression x^2 + 9x - 36?

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x^2 + 9x - 36 can be factored as (x + 12)(x - 3).

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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 primarily for polynomials.

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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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How do you factor the expression 27x^3 + 8?

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27x^3 + 8 can be factored using the sum of cubes formula: (3x + 2)(9x^2 - 6x + 4).