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a. x^2+6x+8/x+4

b. 4x^2+5x-9/x-2

Thanks for your help!!!

a. Note that x^2 + 6x + 8 = (x+4)(x+2); dividing by x+4 cancels them, leaving x+2.

b. Take 4x^2 + 5x - 9 = (x-2)(4x+C).  Multiplying out gives 4x^2 + (C-8)x - 2C.
This doesn't look promising, so try division.

Multiply x-2 by 4x and get 4x^2-8x.  Subtracting off from 4x^2 + 5x - 9 cancels the 4x^2,
and 5x - -8x = 13x, so the result is 13x - 9.

Multiplying x-2 by 13 gives 13x - 26.  Subtracting this from 13x - 9 cancels the 13x terms.
This leaves -9 - -26 = 17.

From this, the result is (4x+13), remainder 17.

Note that (x-2)(4x+13) = 4x^2 + 5x - 26, and the difference is 17, so that is the remainder.


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Scott A Wilson


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