Factoring Polynomials including Grouping and Cubic Equations

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, or factors, that when multiplied together give the original expression.

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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 is the standard form of a polynomial?

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The standard form of a polynomial is written in descending order of the degree of its terms, such as ax^n + bx^(n-1) + ... + k.

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What does it mean to factor a quadratic polynomial?

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Factoring a quadratic polynomial involves expressing it in the form (ax + b)(cx + d), where the product equals the original polynomial.

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What is the difference of squares?

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The difference of squares is a special factoring pattern that states a^2 - b^2 = (a - b)(a + b).

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How do you factor a trinomial of the form ax^2 + bx + c?

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To factor a trinomial of the form ax^2 + bx + c, find two numbers that multiply to ac and add to b, then rewrite the middle term and factor by grouping.

Front

What is the grouping method in factoring?

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The grouping method involves rearranging and grouping terms in a polynomial to factor out common factors from each group.

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What is a cubic polynomial?

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A cubic polynomial is a polynomial of degree three, typically expressed in the form ax^3 + bx^2 + cx + d.

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How do you factor a cubic polynomial?

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To factor a cubic polynomial, look for a common factor, use synthetic division, or apply the Rational Root Theorem to find possible roots.

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What is the Rational Root Theorem?

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The Rational Root Theorem states that any rational solution of a polynomial equation is a factor of the constant term divided by a factor of the leading coefficient.