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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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Can all quadratic expressions be factorised?
Only when the discriminant of the quadratic expression is equal to or greater than zero
What do you do with remainders in quadratic expressions?
Leave it the way it is. (by Stephen Hawking)
Is the foil method used for factoring quadratic equations?
Yes FOIL method can be used with quadratic expressions and equations
What is 2x with the exponent 2 plus 3x plus 1. what is 7n with the exponent 2 plus 9n plus 2. what is 3x with the exponent 2 plus 8x plus 5. what is 7y with the exponent 2 plus 19y plus 10?
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.
What expressions appear as a step in solving 3x2 equal x-5 using the quadratic formula?
The following is the answer:
