Suppose you have the expression x2 + 7x + 12. You look for two numbers that add to 7 and multiply to make 12. They are 3 and 4. You put these numbers into the factors as follows: (x+3)(x+4).
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Here is a harder example. x2 - 5x - 36. The numbers have to multiply to make -36, so one must be negative and the other positive. Since they add to -5, the big number must be negative. If you're stuck, make a list of the pairs of factors of 36: 1x36, 2x18, 3x12, 4x9, 6x6. The numbers we are looking for are 4 and -9, and the factors are (x+4)(x-9).
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These two examples are 'easy' trinomials, since they have no number in front of the x2. 'Hard' trinomials do have a number there. For example, 3x2 - 19x -14. There are several ways of doing this, but it is basically organized trial and error. The factors are (3x+2)(x-7).
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Only when the discriminant of the quadratic expression is equal to or greater than zero
Leave it the way it is. (by Stephen Hawking)
Yes FOIL method can be used with quadratic expressions and equations
The first and third are quadratic expressions in x, the second is a quadratic expressions in n, and the fourth is a quadratic expressions in y. None of them are equations so cannot be solved.
The following is the answer: