Polynomial Factoring

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What is a polynomial?

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A polynomial is a mathematical expression that consists of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication. For example, 3x^2 + 2x - 5 is a polynomial.

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What does GCF stand for in polynomial factoring?

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GCF stands for Greatest Common Factor, which is the largest factor that divides all the terms in a polynomial.

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How do you factor out the GCF from a polynomial?

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To factor out the GCF, identify the largest factor common to all terms, then divide each term by the GCF and write the expression as the GCF multiplied by the resulting polynomial.

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What is factoring by grouping?

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Factoring by grouping is a method used to factor polynomials with four or more terms by grouping terms in pairs, factoring out the common factors, and then factoring the resulting expression.

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What is a trinomial?

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A trinomial is a polynomial with three terms, typically in the form ax^2 + bx + c.

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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, find two numbers that multiply to ac (the product of a and c) and add to b. Rewrite the middle term using these numbers, then factor by grouping.

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What is the difference of squares?

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The difference of squares is a special factoring pattern where a^2 - b^2 can be factored as (a + b)(a - b).

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What is the formula for factoring a perfect square trinomial?

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A perfect square trinomial can be factored using the formula a^2 + 2ab + b^2 = (a + b)^2 or a^2 - 2ab + b^2 = (a - b)^2.

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What does it mean to factor a polynomial completely?

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Factoring a polynomial completely means breaking it down into its simplest factors, which cannot be factored further.

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What is the role of coefficients in polynomials?

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Coefficients are the numerical factors in a polynomial that multiply the variables. For example, in 4x^3, 4 is the coefficient.