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What is the discriminant of a quadratic equation?

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The discriminant is a value calculated from the coefficients of a quadratic equation in the form ax² + bx + c. It is given by the formula D = b² - 4ac. The discriminant determines the nature of the roots of the equation: if D > 0, there are two distinct real roots; if D = 0, there is one real root (a repeated root); if D < 0, there are no real roots.

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How do you complete the square for a quadratic expression?

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To complete the square for a quadratic expression of the form x² + bx, you take half of the coefficient of x (which is b), square it, and add it to the expression. The completed square form is (x + b/2)² - (b²/4).

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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 5x + 4x² + 3x³ - 5x, the degree is 3, as the highest exponent of x is 3.

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How do you determine the number of terms in a polynomial?

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The number of terms in a polynomial is determined by counting the distinct monomials in the expression. For example, in the polynomial (2a - 5)(a² - 1), when expanded, it results in 4 distinct terms.

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What is the standard form of a polynomial?

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The standard form of a polynomial is when the terms are arranged in descending order of their degrees. For example, the standard form of 9x² + 5x + 27 + 2x³ is 2x³ + 9x² + 5x + 27.

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What is a monomial?

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A monomial is a polynomial with only one term. It can be a constant, a variable, or a product of constants and variables raised to non-negative integer powers.

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What is a binomial?

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A binomial is a polynomial that consists of exactly two terms. For example, 3x + 4 is a binomial.

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What is a trinomial?

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A trinomial is a polynomial that consists of exactly three terms. For example, x² + 5x + 6 is a trinomial.

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What is the process of factoring a polynomial?

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Factoring a polynomial involves expressing it as a product of its factors. This can include finding common factors, using special products, or applying methods like grouping.

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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 ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).