Basic Algebra - Factorising

Discussion in 'Algebra' started by moonlighthunter, Mar 7, 2024.

  1. moonlighthunter

    moonlighthunter

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    Hi,
    Expression 1.png
    Expression 1.png The numerator is 9x^2 - 4. According to the exam board the correct answer is b = 4. I think b = 2.
    What do you think?
     
    moonlighthunter, Mar 7, 2024
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  2. moonlighthunter

    HallsofIvy

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    [math]ax^2- b^2= (x\sqrt{a}- b)(x\sqrt{a}+ b)[/math]. That COULD be (3x- 2)(3x+ 2) with a= 9 and b= 2.

    In order that [math]9x^2- 4[/math] reduce to 3x- 2, the denominator must have a factor of 3x+ 2 so must be --- [math](3x+ 2)(4x- 1)= 12x^2 + 5x- 2[/math].

    The fraction is [math]\frac{9x^2- 4}{12x^2+ 5x- 2}[/math] with a= 9, b= 4, c= 12, d= 5, and e= -2.
     
    HallsofIvy, Mar 7, 2024
    #2
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