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Math Help - verifying answers for polynomials

  1. #1
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    verifying answers for polynomials

    I would like to verify that the answers that I have come up with are correct on the following 3 equations. I greatly appreciate it! (the numbers in red are exponents) 1) solve the equation 1/4a2 + 3/4 a=1 My answer is a=4 and a=1 ??? 2) Simplify the expression 2ab4 - 3 a2b2 - ab4 + a2b2 I have ab4 - 2a2b2 ??? and 3) Simplify the expression -2(4y2+3z3+5) + 3(2y2-5z3+3) My answer is -21z3 - 2y2 -1??? I thank you for the help!
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  2. #2
    Super Member bigwave's Avatar
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    latex

    Quote Originally Posted by jay1 View Post
    I would like to verify that the answers that I have come up with are correct on the following 3 equations. I greatly appreciate it! (the numbers in red are exponents) 1) solve the equation 1/4a2 + 3/4 a=1 My answer is a=4 and a=1 ??? 2) Simplify the expression 2ab4 - 3 a2b2 - ab4 + a2b2 I have ab4 - 2a2b2 ??? and 3) Simplify the expression -2(4y2+3z3+5) + 3(2y2-5z3+3) My answer is -21z3 - 2y2 -1??? I thank you for the help!
    hope you learn to use laTex
    this is my understanding of your equation

     <br /> <br />
\frac{1}{4a^2} + \frac{3}{4a} = 1<br />

    \frac{1}{4a^2} + \frac{3}{4a}\times\frac{a}{a}  \Rightarrow \frac{1+3a}{4a^2} = 1

    4a^2 - 3a -1 = 0

    (4a-1)(a+1)= 0

    a= -1

    a=-\frac{1}{4}
    Last edited by bigwave; January 13th 2010 at 12:43 PM.
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  3. #3
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    Is there a place that will show me how to use this "laTex"? BigWave, was my answer correct? Thanks for your help.
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  4. #4
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    Quote Originally Posted by jay1 View Post
    I would like to verify that the answers that I have come up with are correct on the following 3 equations. I greatly appreciate it! (the numbers in red are exponents) 1) solve the equation 1/4a2 + 3/4 a=1 My answer is a=4 and a=1 ??? 2) Simplify the expression 2ab4 - 3 a2b2 - ab4 + a2b2 I have ab4 - 2a2b2 ??? and 3) Simplify the expression -2(4y2+3z3+5) + 3(2y2-5z3+3) My answer is -21z3 - 2y2 -1??? I thank you for the help!

    If problem 1 is what I interpreted it to be, which is this:

    <br />
\frac{1}{4a^2} + \frac{3}{4}a = 1<br />

    then

    <br />
a=1, a=\frac{1+\sqrt{13}}{6}, \text{  and  } a=\frac{1-\sqrt{13}}{6}<br />
.


    However, if problem 1 is this:

    <br />
\frac{1}{4a^2} + \frac{3}{4a} = 1<br />

    then

    <br />
a=1,  a= -\frac{1}{4}<br />
.


    And if problem 1 is this:

    <br />
\frac{1}{4}a^2 + \frac{3}{4}a = 1<br />

    then

    <br />
a=1,  a= -4<br />
.
    Last edited by abender; January 13th 2010 at 12:45 PM. Reason: Including another possibility
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  5. #5
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    Hello, jay1!

    1) Solve: .   \tfrac{1}{4}a^2 + \tfrac{3}{4}a \:=\:1

    My answer: . a=4,\;a=1 . . . . no
    We have: . \tfrac{1}{4}a^2 + \tfrac{3}{4}a \:=\:1

    Multiply by 4: . a^2 + 3a \:=\:4 \quad\Rightarrow\quad a^2 + 3a - 4 \:=\:0

    Factor: . (a-1)(a+4) \:=\:0

    Therefore: . a\;=\;1,\:-4



    2) Simplify: . 2ab^4 -3a^2b^2 - ab^4 + a^2b^2

    I have: . ab^4- 2a^2b^2 . . . . Yes!


    3) Simplify: . -2(4y^2 +3z^3 +5) + 3(2y^2 -5z^3 +3)

    My answer: . -21z^3 - 2y^2 -1 . . . . Right!
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  6. #6
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    PROBLEM 2:

    <br />
2ab^4 - 3 a^2b^2 - ab^4 + a^2b^2 = ab^4 -2a^2b^2<br />

    You are correct.
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  7. #7
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    PROBLEM 3:

    <br />
-2(4y2+3z3+5) + 3(2y2-5z3+3) = (-8y^2 - 6z^3 - 10) + (6y^2 - 15z^3 + 9) = -8y^2 - 6z^3 - 10 + 6y^2 - 15z^3 + 9 = -21z^3 - 2y^2 - 1

    Good job again. Problem 3 is correct.

    -Andy
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  8. #8
    Super Member bigwave's Avatar
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    mystery equation

    who had the mystery equation correct....
    just curious..
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  9. #9
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    Thanks for all of the help. I have a few more that I would like confirmation/correction for (exponents are denoted in red font). It helps to know if I am on the right track. 1) solve the equation x2 + 4x - 45 = 0 I have x=9 and x=-5 ??? 2) find the product of (x-2y)2 I have x2 - 4xy + 4x2 ??? 3) completely factor the expression y2 + 12y + 35 I have come up with (y+7) (y-5)?
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    BigWave, I think that it was Soroban. Thanks again!
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  11. #11
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    Quote Originally Posted by jay1 View Post
    Thanks for all of the help. I have a few more that I would like confirmation/correction for (exponents are denoted in red font). It helps to know if I am on the right track. 1) solve the equation x2 + 4x - 45 = 0 I have x=9 and x=-5 ??? 2) find the product of (x-2y)2 I have x2 - 4xy + 4x2 ??? 3) completely factor the expression y2 + 12y + 35 I have come up with (y+7) (y-5)?

     x^2 + 4x - 45 = 0

     (x+9)(x-5) = 0

     x = 5, -9

    So, reverse the signs for your answer to this problem.
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  12. #12
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    Quote Originally Posted by jay1 View Post
    2) Simplify the expression 2ab4 - 3 a2b2 - ab4 + a2b2 [COLOR=black]I have ab4 - 2a2b2

    <br />
2ab^4 - 3a^2b^2 -ab^4 + a^2b^2 = ab^4 - 2a^2b^2 <br />


    Atta boy (assuming you are a guy).
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  13. #13
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    3) completely factor the expression y2 + 12y + 35 I have come up with (y+7) (y-5)?


    <br />
y^2 + 12y + 35 = (y+7)(y+5) \implies y=-5,-7<br />

    You can always double-check your answers when factoring quadratics by "FOIL"ing.

    Good luck.

    -Andy
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    Perform the indicated operations on this expression: (5a^3 + 3a -2) - (4a^3 + a^2 + 5) I have a^3 + a^2 + 3 Is this right?
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  15. #15
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    Quote Originally Posted by jay1 View Post
    Perform the indicated operations on this expression: (5a^3 + 3a -2) - (4a^3 + a^2 + 5) I have a^3 + a^2 + 3 Is this right?
    No.

    <br />
(5a^3 + 3a -2) - (4a^3 + a^2 + 5) = 5a^3 + 3a - 2 - 4a^3 - a^2 - 5 =<br />
a^3 - a^2 + 3a - 7<br />

    The minus before the parenthesis changes the sign of each term inside the parentheses.

    -Andy
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