1.1 Greatest Common Factor: Vocabulary |
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Factor: A factor is a number, variable or quantity that is being multiplied. |
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Two factors: |
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Three factors: |
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Two factors: |
2 (x+1) |
Two factors: |
(x-3)(x2 + 2x + 1) |
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Factoring, To Factor a Quantity, To Rewrite a Quantity as a Product |
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To rewrite a quantity as factors or to rewrite a quantity as something times something else: |
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The factored form of |
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The factored form of |
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The factored form of |
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Remember, the operation of multiplication holds factors together. |
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Greatest Common Factor (GCF) |
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The largest integer, variable or quantity factor that is a factor of all of the given terms. |
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;GCF = 2 |
;GCF = x |
; GCF = x+1 |
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Integers |
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The counting numbers {1, 2, 3, 4, …}, their negatives, and zero. Mathematicians use the letter to indicate the set of integers. |
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Polynomial |
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A sum or difference of terms, where the exponents are positive integers or 0 and the coefficients are real numbers. The word polynomial comes from Greek words (“polus” and “nomos” ) meaning “many parts.” |
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A polynomial with 4 terms: |
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A polynomial with 2 terms: |
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Not a polynomial: |
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(why?) |
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Product |
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The result obtained from multiplying factors together or the answer to a multiplication problem. |
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6 is the product |
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2x+2 is the product: |
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To “find the product” means to find the result of multiplying factors together. |
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To “rewrite something as a product” to rewrite the quantity as a multiplication problem or as factors. |
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Write 20 as a product: |
Write 2x + 4 as a product:2(x+2) |
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Term: A single number, a single variable or a group of factors. Terms are separated by plus signs, minus signs or equal signs. |
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1 term: |
5 |
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1 term: |
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2 terms: |
3(x+1) + x(x+1)
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1 term: |
a
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4 terms: |
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