Factoring Polynomials

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What does it mean to factor a polynomial?
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Factoring a polynomial involves writing it as a product of its factors or simpler polynomials.
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What's the first step in factoring polynomials?
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The first step is to find the greatest common factor (GCF) of all terms.
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Why is factoring important in algebra?
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Factoring is important because it simplifies expressions and solves polynomial equations.
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What is the GCF of the terms 6x^2 and 9x?
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The GCF is 3x.
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How do you factor the polynomial x^2 + 5x + 6?
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The polynomial factors as (x + 2)(x + 3).
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What is a prime polynomial?
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A prime polynomial is a polynomial that cannot be factored further over the integers.
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What method can be used to factor x^2 - 9?
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This is a difference of squares, which can be factored as (x - 3)(x + 3).
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What is the term for a polynomial like x^2 - 16?
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It is known as a difference of squares.
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Explain the term 'trinomial.'
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A trinomial is a polynomial with three terms.
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How do you factor a polynomial like x^2 + 7x + 10?
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Find two numbers that multiply to 10 and add to 7, which are 5 and 2, then factor as (x + 5)(x + 2).
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What is the first step in factoring x^3 - 3x^2?
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Factor out the common term, x^2, to get x^2(x - 3).
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How do you know if a quadratic trinomial is factorable?
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It is factorable if there are two numbers that multiply to give the last term and add to give the middle term.
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What is the factored form of 2x^2 + 4x?
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The factored form is 2x(x + 2).
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What are the factors of the polynomial x^2 - x - 6?
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The factors are (x - 3)(x + 2).
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Why do we reverse distribution when factoring?
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Reversing distribution helps identify common factors to write the polynomial as a product of simpler polynomials.
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