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?
- To write it as a product of simpler polynomials
- What is the greatest common factor (GCF) of an expression?
- The largest factor shared by all its terms
- Factor out the GCF: 6x + 9
- 3(2x + 3)
- Factor: x^2 - 9
- (x + 3)(x - 3), a difference of squares
- What is the difference of squares factoring pattern?
- a^2 - b^2 = (a + b)(a - b)
- Factor: x^2 + 6x + 9
- (x + 3)^2, a perfect square trinomial
- What is a perfect square trinomial's factored form?
- (a + b)^2 or (a - b)^2
- Factor: x^2 + 5x + 6
- (x + 2)(x + 3)
- What method factors a trinomial with leading coefficient 1, like x^2+bx+c?
- Finding two numbers that multiply to c and add to b
- Factor: x^2 - 7x + 12
- (x - 3)(x - 4)
- Factor: x^2 + x - 6
- (x + 3)(x - 2)
- What is factoring by grouping used for?
- Factoring four-term polynomials by grouping pairs of terms
- Factor by grouping: x^3 + 2x^2 + 3x + 6
- (x^2 + 3)(x + 2)
- What is a prime polynomial?
- A polynomial that cannot be factored into simpler polynomials
- Factor: 2x^2 + 4x
- 2x(x + 2)
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