The Steps of Factoring
Date: 08/08/98 at 10:53:10 From: Brandie Subject: Factoring problems My question concerns the following problems: Given y^2 - 14y + 24 a. write factors of the first term: (______)(_______) b. signs are ________________ because the sign of last term of the trinominal is positive and the sign of the middle term is _________________________: (________________)(________________) c. find factors of 24 whose sum is -14: _____________and___________ d. complete:(___________________)(______________________) I am also have trouble factoring: a^2 + 25a + 24 = (a+1)(a+_______) y^2 - 12y + 27 = (a-3)(a-_______) Please also can you tell me where to go and look for more help on factoring in Algebra I.
Date: 08/14/98 at 13:24:01 From: Doctor Margaret Subject: Re: factoring problems Hi Brandie, Thanks for writing to Dr. Math. It looks as if you are just starting to learn to factor. This is a very nice way of giving a factoring problem because it lists all the things you have to do. It might help for you to remember that the factors of a number are two numbers that when multiplied together give you the number. For example, the factors of 12 are: 1 * 12 2 * 6 3 * 4 In factoring a trinomial we want to get the numbers that, when multiplied together using the FOIL method, give us back the trinomial. There is a method for this. First, we find out the factors of the first term in the trinomial. The factors of y^2 (that's how we write y squared) are y * y. There are two signs in the trinomial between the three terms. The sign on the last term gives us a clue about both of the signs within the parentheses. It would be good if you could memorize: - If the sign on the last term is positive, both signs in the parentheses are the same. - If the sign on the last term is negative, then the signs in the parentheses are different. - If the signs are the same, the first sign will tell you if they are positive or negative. In your first example, we know that both parentheses will contain negative signs. Now let's look at the factors of 24 that will add up to -14. Remember that factors are numbers which in this case multiply together to get 24 and add to get -14. The factors of 24 are: 1 * 24 2 * 12 3 * 8 4 * 6 If we make 2 * 12 into -2 * -12 these numbers multiply to 24 and add to -14: (-2)*(-12) = 24 (-2)+(-12) = -14 Our final answer is: y^2 -14y + 24 = (y -2)(y - 12) We know that this is true because, using FOIL, we get: First: y * y = y^2 Outer: -12 * y = -12y Inner: -2 * y = -2y Last: (-2)*(-12) = 24 So: y^2 -12y -2y + 24 = y^2 - 14y + 24, which is what we started with. Try to do the next two problems by yourself. It would be a good idea to practice a lot. It does get easier, and you will be using it for a long time, so you have to get good at it. There are also some problems in our Dr. Math FAQ: http://mathforum.org/dr.math/faq/faq.learn.factor.html Feel free to write back if you are still having trouble, and try to include any work you've done so we can see exactly where you are stuck. - Doctor Margaret, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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