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Question
15x^4 - 19x^2 + 6 =
(x + 18)(x - 11)(x + 12) > 0
I will take it you are trying to factor the first expression.
The quadratic gives x²=(19±√(361-4*6*15))/30.
Note that 4*6*15 is 360, so the answer is (19±1)/30.
To actually factor it out, it's 15(x - 2/3)(x - 3/5).
For the second one, construct a table with -∞ -18 -12 11 ∞ that has lines below -18, -12, and 11. Make a three horizontal lines and in each box below, and at the left side of each row put x+18m x-11, and x+12. In each of the cells, put a + if the term is positive and a - if the term is negative.
I have sent what I am talking about with the
vertical lines as -18, -12, and 11.
x+18 - | + | + | +
x-11 - | - | - | +
x+12 - | - | + | +
To get the sign of the function, multiply each column. Remeber that age old rule "two negatives make a positive" and you will get the results. Note that the sign is alternating. If you don't get that, it's a rework.
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Scott A Wilson
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I earned high honors in both my BS degree and MS degree from Oregon State.
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