i need some algebra help: factoring
07-26-2009, 09:50 PM
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i need some algebra help: factoring ok im tired and cant understand the book's examples, can anyone help its probably not too difficult i just dont get it
EX. 4x^2-32x+15, factor out completly??
this sucks
EX. 4x^2-32x+15, factor out completly??
this sucks
07-26-2009, 10:19 PM
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The quadratic equation gives you roots of 7.5 and 0.5, so your factors will be:
(x-7.5)(x-0.5). Notice that when you expand, this gives you the same result as if you divided your original equation by four.
Alternatively, notice that your first component (4x^2) can be formed by multiplying either x*4x, or 2x*2x, so the first part of each factor will be one of these. The last is a positive 15, which can be formed by multiplying 1*15 or 3*5.
Because the first term is positive (4x^2), the first terms in each factor must be either both positive or both negative. The last term is positive (15), so same case: the second terms must be either both positive or both negative. The middle term (-32x) makes the sign determination. In this case, it is negative, so your signs will both be negative.
Now you have to organize the possible factors and see which one will give you the original equation via FOIL (first, inner, outer, last). The correct one is:
(2x - 15)(2x - 1). Notice that if you divide by two, you get the same result as when using the quadratic equation.
Sorry for the lengthy reply; it's much easier to do this in person/on paper. Hopefully it was clear enough to help; it's been a while since I've taken an algebra class.
07-27-2009, 08:40 AM
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You can use the quadratic equation or factor by using the FOIL method backwards.
The quadratic equation gives you roots of 7.5 and 0.5, so your factors will be:
(x-7.5)(x-0.5). Notice that when you expand, this gives you the same result as if you divided your original equation by four.
Alternatively, notice that your first component (4x^2) can be formed by multiplying either x*4x, or 2x*2x, so the first part of each factor will be one of these. The last is a positive 15, which can be formed by multiplying 1*15 or 3*5.
Because the first term is positive (4x^2), the first terms in each factor must be either both positive or both negative. The last term is positive (15), so same case: the second terms must be either both positive or both negative. The middle term (-32x) makes the sign determination. In this case, it is negative, so your signs will both be negative.
Now you have to organize the possible factors and see which one will give you the original equation via FOIL (first, inner, outer, last). The correct one is:
(2x - 15)(2x - 1). Notice that if you divide by two, you get the same result as when using the quadratic equation.
Sorry for the lengthy reply; it's much easier to do this in person/on paper. Hopefully it was clear enough to help; it's been a while since I've taken an algebra class.
The quadratic equation gives you roots of 7.5 and 0.5, so your factors will be:
(x-7.5)(x-0.5). Notice that when you expand, this gives you the same result as if you divided your original equation by four.
Alternatively, notice that your first component (4x^2) can be formed by multiplying either x*4x, or 2x*2x, so the first part of each factor will be one of these. The last is a positive 15, which can be formed by multiplying 1*15 or 3*5.
Because the first term is positive (4x^2), the first terms in each factor must be either both positive or both negative. The last term is positive (15), so same case: the second terms must be either both positive or both negative. The middle term (-32x) makes the sign determination. In this case, it is negative, so your signs will both be negative.
Now you have to organize the possible factors and see which one will give you the original equation via FOIL (first, inner, outer, last). The correct one is:
(2x - 15)(2x - 1). Notice that if you divide by two, you get the same result as when using the quadratic equation.
Sorry for the lengthy reply; it's much easier to do this in person/on paper. Hopefully it was clear enough to help; it's been a while since I've taken an algebra class.
..it was a take home test btw
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07-27-2009, 09:24 PM
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07-28-2009, 11:21 AM
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07-29-2009, 02:09 PM
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Be careful about the cops up there. I almost had to get a lawyer on retainer to cover my tickets.
