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  1. #1
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    3 questions

    Solve the following inequality. Write the answer in interval notation.
    Note: If the answer includes more than one interval write the intervals separated by the "union" symbol, U. If needed enter as infinity and as -infinity .




    Find the quotient and remainder using long division for






    Simplify the expression
    and give your answer in the form of

    Your answer for the function is :
    Your answer for the function is :
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  2. #2
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    Quote Originally Posted by wannous View Post
    Solve the following inequality. Write the answer in interval notation.
    Note: If the answer includes more than one interval write the intervals separated by the "union" symbol, U. If needed enter as infinity and as -infinity .




    Find the quotient and remainder using long division for








    Simplify the expression



    and give your answer in the form of



    Your answer for the function is :


    Your answer for the function is :
    For Q.3 note that

    7x^3 - 8x^2 - 12x = x(x-2)(7x+3)

    and

    6x^2 - 16x + 8 = 2(x - 2)(3x - 2).


    So \frac{7x^3 - 8x^2 - 12x}{6x^2 - 16x + 8} = \frac{x(x-2)(7x+3)}{2(x - 2)(3x - 2)}

     = \frac{x(7x + 3)}{2(3x - 2)}.


    Therefore f(x) = x(7x + 3) and g(x) = 2(3x - 2).
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  3. #3
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    Hello wannous
    Quote Originally Posted by wannous View Post
    Solve the following inequality. Write the answer in interval notation.
    Note: If the answer includes more than one interval write the intervals separated by the "union" symbol, U. If needed enter as infinity and as -infinity .

    To solve this type of inequality, find the values of x that make each factor zero, and then look at their signs as x moves along the number line from left to right, through each of these 'zero values' in turn.

    Now the 'zeros' occurs when x =4 and x=5. So we look at what happens when:

    • x<4


    • 4<x<5


    • 5<x

    First, if x<4,\, (x-5) is negative and (x-4) is also negative; and -^{ve}\times -^{ve} = +^{ve}. So (x-5)(x-4)>0 in this range.

    Next, if 4<x<5,\, (x-5) is -^{ve} and (x-4) is +^{ve}; -^{ve}\times+^{ve} = -^{ve}. So (x-5)(x-4) < 0 in this range.

    Finally, if x>5, we get +^{ve}\times+^{ve}=+^{ve}. So (x-5)(x-4)>0 in this range.

    So the values we want are 4\le x \le 5, or in interval notation [4,5].


    Find the quotient and remainder using long division for

    See the attached image.

    So the quotient is
    x^2-4x+1 and the remainder is -5.

    Grandad


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