x^2-7x+12
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The answer is (x-3)(x-4).
You basically have to write down the factors of 12. Two of these factors should either add together or one should take away from he other to make -7. The positive sign before the 12 tells you you need to add (i.e both signs should be the same).
Here isthe working:
Factors of 12: 1 2 3 Write them out as they would multiply to make 12 vertically.
12 6 4
The only pair which can make 7 is 3 and 4. As I already mentioned, the positive sign before the 12 means both signs must be the same (e.g you can't have +3-4, it must be +3+4 or -3-4). You want to make -7, so it has to be -3 and -4 you use. These are the numbers which go in the brackets of you final answer. Because it is x^2, it will be x times x. This means the brackets will be (x-3)(x-4).
If you want to check that your answer is right, use the FOIL rule, which means you multiply in this order:
Firsts
Outers
Inners
Lasts
i.e if you have (x-3)(x-4), then you multiply the x's first, as they are the first terms in the brackets. Then the outer numbers, (x and -4), the inner numbers (x and -3) and then the last numbers (-3 and -4). If you do this, you get x^2 - 3x - 4x + 12, which can simplify back to the original question, meaning the answer is right.
Hope it makes sense, I'm not good at explaining things!
Anon :)
You basically have to write down the factors of 12. Two of these factors should either add together or one should take away from he other to make -7. The positive sign before the 12 tells you you need to add (i.e both signs should be the same).
Here isthe working:
Factors of 12: 1 2 3 Write them out as they would multiply to make 12 vertically.
12 6 4
The only pair which can make 7 is 3 and 4. As I already mentioned, the positive sign before the 12 means both signs must be the same (e.g you can't have +3-4, it must be +3+4 or -3-4). You want to make -7, so it has to be -3 and -4 you use. These are the numbers which go in the brackets of you final answer. Because it is x^2, it will be x times x. This means the brackets will be (x-3)(x-4).
If you want to check that your answer is right, use the FOIL rule, which means you multiply in this order:
Firsts
Outers
Inners
Lasts
i.e if you have (x-3)(x-4), then you multiply the x's first, as they are the first terms in the brackets. Then the outer numbers, (x and -4), the inner numbers (x and -3) and then the last numbers (-3 and -4). If you do this, you get x^2 - 3x - 4x + 12, which can simplify back to the original question, meaning the answer is right.
Hope it makes sense, I'm not good at explaining things!
Anon :)
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The factors of a trinomial are going to be two binomials
They will have the form
(ax+b) and (cx+d)
where ac will equal the multiplier for the x^2 variable, in your case 1
where ad+bc will equal the multiplier for the x^1 variable, in your case -7
and where bd will equal the multiplier for the x^0 variable, in your case +12
As the factors of 1 are 1 and 1 then our factors start to shape up as
(1x+b) and (1x+d) or
(x+b) and (x+d)
They will have the form
(ax+b) and (cx+d)
where ac will equal the multiplier for the x^2 variable, in your case 1
where ad+bc will equal the multiplier for the x^1 variable, in your case -7
and where bd will equal the multiplier for the x^0 variable, in your case +12
As the factors of 1 are 1 and 1 then our factors start to shape up as
(1x+b) and (1x+d) or
(x+b) and (x+d)
12
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