Math help

I need help on these problems. There over solving equations by factoring.

1. 4x^2=9

2. M^2-36=16M

3. R^2+9=10r

4. 6s^2=17s-12

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  1. set everything to zero, then you can factor.

    #4
    6s^2-17s+12 = 0
    You know the factors will look like
    (6x-?)(x-?) or (3x-?)(2x-?)
    So, since -17 is fairly large, we will probably have the first
    (6s-3)(s-4) gives -27s too big
    (6s-4)(s-3) gives -22s still too big
    (6s-6)(s-2) gives -18s close, but no cigar
    (3s-4)(2s-3) gives -17s YES!

    Do the others the same way. #1 involves a difference of squares, so it's easy.

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    posted by Steve
  2. Would #4 be s=1 and s=2?

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  3. well, no.
    If the product of some numbers is zero, then one of the numbers must be zero. We have

    (3s-4)(2s-3) = 0
    So, we must have either
    3s-4 = 0
    or 2s-3 = 0

    So, s = 4/3 or 3/2

    Had you tried your guesses in the original equation, you would have seen they did not satisfy it.

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    posted by Steve

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