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16 Cards in this Set
- Front
- Back
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Factoring is a process of:
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transferring an algebraic expression into the products of two or more simple expressions, called factors.
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The Greatest Common Factor of integers is:
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The greatest integer that can evenly divide all of these integers.
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What are the steps for using the long division method to obtain the G.C.F.?
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Divide all the integers by a number that goes into ALL of them (unlike finding L.C.D. where the divisor only has to go into 2 of them). Repeat as long as the divisor goes into ALL the integers. The product of the divisors is the G.C.F.
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The Greatest Common Factor for terms with variables is:
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the factor with the smallest exponent that is common to all.
ie. The G.C.F. of X³, X⁵, and X⁷ = X³ ; The G.C.F. of X⁴Y², XY³, and X²Y⁵ = xy² |
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The Greatest Common Factor of an algebraic expression consisting of integers and variables is:
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The product of the greatest common factors of the integers and the variables.
ie. The G.C.F. of 12x⁴y², 18xy³, and 24x²y⁵ = 6xy² |
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What are the guidelines for factoring a trinomial by the cross product multiplication method?
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For example: x² + 5x + 6
1) If the constant term of a trinomial is positive (the 6 in the above example), the possible factors for the answers should be those with the same sign as the coefficient of the x of the trinomial (5 above). 2) If the constant term of a trinomial (6 above) is negative, the possible factors for the answer should have opposite signs. |
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What are the steps for factoring a trinomial using the cross product multiplication method?
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1) Arrange the trinomial in descending order from highest exponent to lowest.
2) Resolve the first and third term into the product of all possible factors. 3) Select one pair of factors for the first term and align them into a vertical column. Do the same for a pair of factors for the third term. 4) Cross multiply these factors and add their products. If successful, the sum will be exactly the same as the middle term. If unsuccessful, first try switching the factors in the column for the third term before trying other factors. |
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A quadratic equation is an equation with a degree of:
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2
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Quadratic equation standard form:
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ax² + bx + c = 0
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If the second or third term of the quadratic equation is not present, the coefficient of that term is considered to be:
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zero
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A quadratic equation with either the second or third terms (or both) equal to zero is called:
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incomplete quadratic equations
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The factoring method of solving quadratic equations is based on this:
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the zero-factor property
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Describe the zero-factor property
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If a and b are real numbers and if ab = 0, then a = 0 or b = 0, or both a and b are 0.
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Steps to solve a quadratic equation by factoring:
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1) Write the equation in standard form.
2) Factor the trinomial or binomial. 3) Set each factor equal to 0 and solve the resulting equation. |
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When factoring a term such as 2x² = 4x, one should be careful. Why?
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It is common to make the mistake of dividing both sides by 2x, leaving the answer x = 2. This is incorrect because without solving the quadratic properly, one root is left out; in this case, x = 0.
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Solve for x:
2x² - 2x - 4 = 0 |
x = 2 or x = -1
(you can cancel out the 2 by dividing both sides by 2.) p. 239 # 37 |
