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Thread: factoring

  1. #1
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    factoring

    Please Help!

    1.)Factor the expression: $\displaystyle 4y^2-49$
    2.)Factor the expression completely: $\displaystyle 2x^2-16xy+32y^2$
    3.)Solve the equation: 4x^2-2x=0
    4.)The length of a rectangular garden is 25 feet longer than the width. If it covers an area of 2600 sq. ft., find the length and width.
    5.)x and y vary inversely. If x=2.4 when y=130, find and equation relating x and y.
    6.)Find the domain of the rational expression: $\displaystyle x^2+4 (over) x^2+4x$
    7.)Simplify: $\displaystyle 3x^3(y-3) (over) 5y^2x^2$
    8.) Divide $\displaystyle (15A^3-12A^2-9A)/3A^2$
    9.) Is a function defined by {(-2,3), (0,1), (2,-2), (4,2)}? If so state it's domain.
    10.) $\displaystyle f(x)=-2x^2+7x+5$ Find $\displaystyle f (3/2)$
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  2. #2
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    And the last of it!
    1.)Find the equation for the linear function:
    $\displaystyle f(4)=-1$ $\displaystyle f(-2)=-4$
    2. Sketch the graph of $\displaystyle f(x)=2x+1$
    3. Sketch the graph of $\displaystyle f(x)=(2/3)x-3$
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  3. #3
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    Quote Originally Posted by jscalalamoboy View Post
    Please Help!

    1.)Factor the expression: $\displaystyle 4y^2-49$
    2.)Factor the expression completely: $\displaystyle 2x^2-16xy+32y^2$
    3.)Solve the equation: 4x^2-2x=0
    4.)The length of a rectangular garden is 25 feet longer than the width. If it covers an area of 2600 sq. ft., find the length and width.
    5.)x and y vary inversely. If x=2.4 when y=130, find and equation relating x and y.
    6.)Find the domain of the rational expression: $\displaystyle x^2+4 (over) x^2+4x$
    7.)Simplify: $\displaystyle 3x^3(y-3) (over) 5y^2x^2$
    8.) Divide $\displaystyle (15A^3-12A^2-9A)/3A^2$
    9.) Is a function defined by {(-2,3), (0,1), (2,-2), (4,2)}? If so state it's domain.
    10.) $\displaystyle f(x)=-2x^2+7x+5$ Find $\displaystyle f (3/2)$
    Quote Originally Posted by jscalalamoboy View Post
    And the last of it!
    1.)Find the equation for the linear function:
    $\displaystyle f(4)=-1$ $\displaystyle f(-2)=-4$
    2. Sketch the graph of $\displaystyle f(x)=2x+1$
    3. Sketch the graph of $\displaystyle f(x)=(2/3)x-3$


    You will have to show some work... You will learn only if you work out and get stuck somewhere. We will tell you how to continue....
    Lets start:

    1)Factor the expression: $\displaystyle 4y^2-49$

    Hint:
    $\displaystyle 4y^2-49 = (2y)^2 - 7^2$. Hmm it looks familiar.... Have you ever seen what $\displaystyle a^2 - b^2$ is?

    2.)Factor the expression completely: $\displaystyle 2x^2-16xy+32y^2$

    Hint: Let $\displaystyle u = \frac{x}{y}$, then $\displaystyle x = uy$
    $\displaystyle 2x^2-16xy+32y^2 = 2((uy)^2 - 8(uy)y + 16y^2) = 2y^2(u^2 - 8u^2 + 16)$

    Does $\displaystyle (u^2 - 8u^2 + 16) = u^2 - 2(u)(4) + (4)^2$ remind you of anything?

    3.)Solve the equation: $\displaystyle 4x^2-2x=0$

    Hint: $\displaystyle 4x^2-2x=0 \Rightarrow 2x(2x-1) = 0$
    Use this fact: for real numbers a and b, if ab = 0, then a=0 or b=0

    4)The length of a rectangular garden is 25 feet longer than the width. If it covers an area of 2600 sq. ft., find the length and width.

    Hint: Denote length by l and width by w.

    $\displaystyle l = 25+w$

    $\displaystyle Area = 2600$

    $\displaystyle lw = 2600$

    $\displaystyle (25+w)w = 2600$

    $\displaystyle w^2 + 25w - 2600 = 0$

    Now solve the quadratic...

    Try these... If you did not understand anything.. ask
    Then I will help you with remaining...

    Good luck
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