Algebra 1, Unit 7: Factoring. Key terms, formulas, and worked-example cues a high school student meets for this unit, building on prior units. Front: the term, formula name, or short problem cue. Back: the definition, formula, or solution method.
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- What does it mean to 'factor' a polynomial?
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To write it as a product of simpler polynomials- What is the greatest common factor (GCF) of an expression?
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The largest factor shared by all its terms- Factor out the GCF: 6x + 9
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3(2x + 3)- Factor: x^2 - 9
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(x + 3)(x - 3), a difference of squares- What is the difference of squares factoring pattern?
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a^2 - b^2 = (a + b)(a - b)- Factor: x^2 + 6x + 9
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(x + 3)^2, a perfect square trinomial- What is a perfect square trinomial's factored form?
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(a + b)^2 or (a - b)^2- Factor: x^2 + 5x + 6
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(x + 2)(x + 3)- What method factors a trinomial with leading coefficient 1, like x^2+bx+c?
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Finding two numbers that multiply to c and add to b- Factor: x^2 - 7x + 12
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(x - 3)(x - 4)- Factor: x^2 + x - 6
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(x + 3)(x - 2)- What is factoring by grouping used for?
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Factoring four-term polynomials by grouping pairs of terms- Factor by grouping: x^3 + 2x^2 + 3x + 6
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(x^2 + 3)(x + 2)- What is a prime polynomial?
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A polynomial that cannot be factored into simpler polynomials- Factor: 2x^2 + 4x
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2x(x + 2)
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