3x^2 + x - 4 = 0leskiSeptember 11 2006, 18:15:59 UTC
Factoring: Yes, it's pretty much guesswork to factor stuff like this... you start with (3x...)(x...) and try and figure out what the rest is... well, -4 is either (-4)(1), (4)(-1) or (2)(-2)... though when you're trying these different combinations, you don't need to FOIL the entire equation each time to see if it's right; you know that the x^2 (First) and the constant term (Last) will be right (because you've already picked numbers that will multiply together to give that), it's just the x that you're worried about, so you only need to do the Outer and Inner parts to check if you're right.
ex. Is it (3x+2)(x-2)? Outer = (3x)(-2) = -6x, Inner = (2)(x)= 2x, which gives a middle term of -6x + 2x = -4x. No. Is it (3x-1)(x+4)? O = 12x, I = -x, so we'd get 11x. No. Is it (3x+4)(x-1)? O + I = -3x + 4x = x. Yes.
Shortcut: Quadratic FormulaIf you just need to find the solution(s) to the formula, use the quadratic formula
( ... )
Sounds like a great night out ! And just like the polkaroo, I missed it.. I think someone wrote a big thing on factoring so I'll leave it be for the moment.
Comments 13
was wondering why there hadn't been any posts in a long time . . .
xoxoxo
steve
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Yes, it's pretty much guesswork to factor stuff like this... you start with (3x...)(x...) and try and figure out what the rest is... well, -4 is either (-4)(1), (4)(-1) or (2)(-2)... though when you're trying these different combinations, you don't need to FOIL the entire equation each time to see if it's right; you know that the x^2 (First) and the constant term (Last) will be right (because you've already picked numbers that will multiply together to give that), it's just the x that you're worried about, so you only need to do the Outer and Inner parts to check if you're right.
ex.
Is it (3x+2)(x-2)? Outer = (3x)(-2) = -6x, Inner = (2)(x)= 2x, which gives a middle term of -6x + 2x = -4x. No.
Is it (3x-1)(x+4)? O = 12x, I = -x, so we'd get 11x. No.
Is it (3x+4)(x-1)? O + I = -3x + 4x = x. Yes.
Shortcut: Quadratic FormulaIf you just need to find the solution(s) to the formula, use the quadratic formula ( ... )
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