#$&*
Mth 158
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
Factoring a Trinomial
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I'm not sure about these questions on factoring trinomials. The example in the book is: X^2 + 7X + 10 = (X+2)(X+5)
I'm not sure how that factored out?
@&
If you multiply (x+2)(x+5) you get
x ( x + 5) + 2 ( x + 5) =
x^2 + 5 x + 2 x + 10.
You get x^2 from x * x, and this matches the x^2 in the given trinomial x^2 + 7 x + 10.
The 5x and the 2x add up to 7x, which matches the 7x in the given trinomial.
The 10, which came from 2 * 5, matches the 10 in the given trinomial.
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That verifies that the factoring is correct, but it doesn't completely address how you would find that result.
If a trinomial starting with just plain x^2 is to factor, then it has to factor into the form
(x + ?) * (x + ?),
because when you distribute this will give you the x^2.
Applying this to
x^2 + 7 x + 10
we need to find the ? values so that
(x + ?) ( x + ?) = x^2 + 7 x + 10.
The two ? mark values are the ones that will give you 10, when they are multiplied. The only ways to get 10 using integers are 1 + 10, -1 * (-10), 2 * 5 and -2 * (-5).
So if the trinomial factors it will be one of the following:
(x + 1) ( x + 10)
(x - 1) ( x - 10)
(x + 2) ( x + 5 )
(x - 2) ( x - 5).
It won't hurt right now to multiply all these out, but of course once we get used to the process we'll be able to see right away that some possibilities just won't work.
You should verify that
(x + 1) ( x + 10) = x^2 + 11 x + 10
(x - 1) ( x - 10) = x^2 - 11 x + 10
(x + 2) ( x + 5 ) = x^2 + 7 x + 10
(x - 2) ( x - 5) = x^2 - 7 x + 10.
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We see that the third possibility gives us the trinomial x^2 + 7 x + 10.
It is very possible that a given trinomial won't factor. For example if the given trinomial had been x^2 + 5 x + 10, none of the possibilities would have worked.
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There is more to the factoring of trinomials, but this should help you get through the most basic problems. We can address more difficult problems later, if you need to do so (and if you ask).
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#$&*
Mth 158
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
Rational Expressions
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I find reducing a rational expression to lowest terms kind of diffifult. I cant even get past writing down the problem without getting confused.
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Your question isn't very specific. Examples of the first problems that give you trouble would be helpful.
So I'm guessing about what sort of example might be most helpful. Let's try this:
(x^2 + 7 x + 10) / (x^2 + 4 x + 4).
The numerator of this expression factors as (x+2)(x+5), while the denominator factors as (x+2)(x+2), or (x+2)^2.
So we have
(x^2 + 7 x + 10) / (x^2 + 4 x + 4) =
(x+2)(x+7) / ( (x+2)(x+2) ).
Now the x+2 in the numerator can be divided by one of the x+2 terms in the denominator, leaving us with
(x + 7) / (x + 2).
Let me know if this is the sort of thing you're asking about. Feel free to ask additional questions about this topic. Remember that examples to show more specifically what you are referring to can be very helpful.
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#$&*
Mth 158
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
Complex Rational expressions
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I'm not sure how to work these out. I think it's mainly because just looking at the problem is intimidating.
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There are a number of possible expressions of this type. I'll have to ask you to narrow your question down by providing me with one or two examples of the sorts of expressions you're asking about.
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There are a number of possible expressions of this type. I'll have to ask you to narrow your question down by providing me with one or two examples of the sorts of expressions you're asking about.
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#$&*
Mth 158
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
Single Quotients
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This problem is confusing. (X^2+1)^1/2 + X*1/2(X^2+1)^-1/2*2X
I dont know how to work anything out.
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I'm not sure what your expression means or what you're asked to do with it.
The expression itself doesn't appear to be in good form. The second term has x as a factor twice, once at the beginning and once at the end.
Could you mean the following?
( (X^2+1)^1/2 + X ) * (1/2(X^2+1)^-1/2) * 2X
In any case I'll take a look at the textbook tomorrow and see if I can find something similar to this expression.
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