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Math Help - All About Fractoring Algebraic Equations

  1. #1
    Newbie RyanCouture's Avatar
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    All About Fractoring Algebraic Equations

    Hey guys, first post here (hopefully the last) - in a good way

    Anyway, I'm doing a mail-in correspondance course for grade 12 college math, and I have to have this thing completed within the next day. I breezed through 19 of 20 lessons, and now my arch enemy has returned.

    I don't know if its so much that I can't understand it, as it is just very poorly demonstrated and explained in the book here (having no teacher certainly makes things harder). Anyway, I got about 9 questions here that I need you folks to help me out with. I'm just gonna scan em' right from the book.



    There you go, I need help with #83-#85. Any help is welcomed.

    Thanks guys.
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  2. #2
    Newbie RyanCouture's Avatar
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    wow FYI boys check out this site

    QuickMath Automatic Math Solutions
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by RyanCouture View Post
    wow FYI boys check out this site

    QuickMath Automatic Math Solutions
    1. We know

    2. It does not tell you why, which is the purpose of maths education.

    RonL
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by RyanCouture View Post
    Hey guys, first post here (hopefully the last) - in a good way

    Anyway, I'm doing a mail-in correspondance course for grade 12 college math, and I have to have this thing completed within the next day. I breezed through 19 of 20 lessons, and now my arch enemy has returned.

    I don't know if its so much that I can't understand it, as it is just very poorly demonstrated and explained in the book here (having no teacher certainly makes things harder). Anyway, I got about 9 questions here that I need you folks to help me out with. I'm just gonna scan em' right from the book.



    There you go, I need help with #83-#85. Any help is welcomed.

    Thanks guys.
    83 (a) Factor m^2+5m+6.

    Suppose:

    m^2+5m+6=(m+a)(m+b)

    Then a+b=5 and ab=6.

    So we try the factors of 6 as possible values of a and b, and find that a=2 and b=3 will do, so:

    m^2+5m+6=(x+2)(x+3).

    RonL
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  5. #5
    Grand Panjandrum
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    83 (b) Factor p^2-pq -12q^2

    Here we are looking for a factorisation of the form:

    p^2-pq -12q^2=(p+aq)(p+bq),

    so ab=-12, and a+b=-1.

    Now we try the factors of -12 for a and b. These are 1,\ -1,\ 12,\ -12,\ 2,\ -2,\ 3,\ -3,\ 4,\ -4,\ 6,\ -6. Of these -4 and 3 seem to work, and so:

    p^2-pq -12q^2=(p-4q)(p+3q)

    RonL
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  6. #6
    Grand Panjandrum
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    83 (c) Factor 12x^2+19x-18

    Write:

    <br />
12x^2+19x-18=(ax+b)(cx+d)<br />

    Then -18=bd and 12=ac, so we try the factors
    of -18 for b and d and the factors of 12 for a and c.

    If you run through all of these you wil be here all day.

    A short cut is to use the quadraic formula since if:

    <br />
12x^2+19x-18=(ax+b)(cx+d)<br />

    then the roots of 12x^2+19x-18=0 are -d/c and -b/a, but the roots are:

    <br />
x=\frac{-19 \pm \sqrt{19^2+4\times 12 \times 18}}{2\times 12}=\frac{-9}{4} \mbox{ or } \frac{2}{3}<br />

    So we try b=-2 and a=3, and we find that:

    <br />
12x^2+19x-18=(3x-2)(4x+9)<br />

    RonL
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  7. #7
    Grand Panjandrum
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    84 (a) Factor 9y^2-100

    This is the difference of two squares and you should know the factorisation
    of such expressions:

    <br />
(a^2-b^2)=(a+b)(a-b)<br />

    84 (b) Factor 7p^2+19p-6

    is like 83 (c), but as 7 is prime we know if this has a "nice" factorisation it is of the form:

    7p^2+19p-6=(7p+a)(p+b)

    and trial and error will quickly show that:

    7p^2+19p-6=(7p-2)(p+3)

    RonL
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  8. #8
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    Quote Originally Posted by CaptainBlack View Post
    83 (c) Factor 12x^2+19x-18
    \begin{aligned}12x^2+19x-18&=&12x^2+(27x-8x)-18\\&=&(12x^2-8x)+(27x-18)\\&=&4x(3x-2)+9(3x-2)\\&=&(3x-2)(4x+9)\end{aligned}

    Quote Originally Posted by CaptainBlack View Post
    84 (b) Factor 7p^2+19p-6
    \begin{aligned}7p^2+19p-6&=&7p^2+(21p-2p)-6\\&=&7p(p+3)-2(p+3)\\&=&(p+3)(7p-2)\end{aligned}

    Another ways
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