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April 17th, 2011, 04:24 PM   #1
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Solving Cubic Equations

Consider the polynomial
p(x)=x+ax+bx-12
Given that (x+3) and (x-4) are factors of p(x), factorise p(x) completely.

I'm not sure whether I should sub in -3 and 4 or whether I should divide the original polynomial by x+3 and x-4.
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April 17th, 2011, 05:09 PM   #2
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Re: Solving Cubic Equations

Hello, chris99191!

Quote:




I'm not sure whether I should sub in -3 and 4 or whether I should divide the original polynomial by x+3 and x-4.
[color=blue]Both methods should work . . .[/color]

This is how I solved it . . .



[color=beige]. . [/color]


[color=beige]. . [/color]










[color=beige]. . [/color]

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April 17th, 2011, 06:06 PM   #3
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If x + ax + bx - 12 ? (x + 3)(x - 4)(x + r), putting x = 0 gives r = 1.
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