The factors to your equation are:
(X + 3) x (X + 12)
I did this by just looking at it. The way I do these, (for equations where the coeffiecient of the X^2 term is 1) is I think of all the sets of factors for the last term (36) and see if there are any that add to 15. In this case 3 x 12 =36 and 3 + 12 = 15. For equations where the X^2 term has a number other than 1 it gets a little more complicated, because this affects the way the factors "add" in the creation of the the middle term of the equation, but has no effect on the last term. For these equations, I still think of all the factors of the last term, but keep in mind that either of these factors could be being multiplied by the coeficient of the "x" term. For example, the equation: 2x^2 + 27x + 36 would have the factors: (2X + 3) x (X + 12). For the equation 2X^2 + 18X + 36 the factors are (2X + 12) + (X + 3). Note how interchanging the positions of the numbers in the factors changes the middle term. Some other hints: if the last term is positive, either both signs between the terms of each of the factors are positive, or both are negative. If the last term is negative, one of these signs is negative. When one sign is negative, the middle number can be either positive or negative.
You might get a better idea of the relationship between the factors and the resulting equations if you do just the opposite of what they tell you to do for your homework; make some factors and multiply them to make the resulting equations. Try ones where there are negative signs for either the "X" part, or the number part of the factor. Examples: (X - 7), (2X + 13), (-X - 3), (-3X + 5) etc.
2007-11-18 11:21:52
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answer #1
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answered by Flying Dragon 7
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Usually in typed form x squared is written x^2. The symbol ^ means to the power of so 3^4 would be 3 to the power of 4.
You can also use extra characters from a word processor to include the symbol ² but most people just use ^
Now to answer your question. To factorise this you need to think of two numbers which multiple to give 36 and which add to give 15.
Lets try a few pairs:
1×36 = 36 but 1+36≠15 so can't be those two.
2×18 = 36 but 2+18≠15 so can't be those two.
3×12 = 36 and 3+12=15 so these are the numbers we need.
So x²+15x+36 = (x+3)(x+12) (the two numbers we found above)
2007-11-18 10:37:08
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answer #2
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answered by Anonymous
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Simplifying
x^2 + 15x + 36 = 0
Reorder the terms:
36 + 15x + x^2 = 0
Solving
36 + 15x + x^2 = 0
Solving for variable 'x'.
Factor a trinomial.
(12 + x)(3 + x) = 0
Subproblem 1
Set the factor '(12 + x)' equal to zero and attempt to solve:
Simplifying
12 + x = 0
Solving
12 + x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12
Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12
Combine like terms: 0 + -12 = -12
x = -12
Simplifying
x = -12
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:
Simplifying
3 + x = 0
Solving
3 + x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3
Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3
Combine like terms: 0 + -3 = -3
x = -3
Simplifying
x = -3
Solution
x = {-12, -3}
2007-11-18 10:38:15
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answer #3
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answered by Anonymous
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It's not an expression it has an equal sign it's an equation so i'm thinking it says solve
to factorize x² + 15x +36 however
since in form x² +bx + c
1. find factors of c that when you add then you get b and mutliply then u get c
factors are 3 and 12
2. replace the term with b using these factors
x² + 3x + 12x + 36
3. factor by grouping
x(x+3) + 12(x+3)
then factor completely
(x+3)(x+12)
to solve we have (x+3)(x+12)=0
which means (x+3)=0 or (x+12)=0
x = - 3 or x= - 12
you can always check by substituting into the original equation
2007-11-18 10:41:06
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answer #4
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answered by smpbizbe 2
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1st of all that isnt an expression.we
X2+3(5)+2 2 3 3=0
the 2 next to the x is an exponent
the second 2 in 2 2 3 3 is an exponent
and the second3 in 2 2 3 3 is an exponent.
the equation looks like its factorized already
2007-11-18 10:38:06
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answer #5
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answered by uchiha 2
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(X+3)(X+12) since its only X^2, you only have to put x, and ask for the 3 and 12, 3x12=36, and then when you check your work, you come out with the equation X^2+15X+36! yay!
2007-11-18 10:35:14
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answer #6
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answered by Anonymous
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Find the factors of 36.
36= 1, 2, 3, 4, 6, 9, 12, 18, 36
The two factors must add up to 15, so 12 and 3 are the factors that add up to 15.
(x+3)(x+12)=0
Set each binomials to zero and simplify.
x+3=0
x=-3
x+12=0
x=-12
x={-3, -12}
Here are your answers!
2007-11-18 10:34:20
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answer #7
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answered by Anonymous
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completing the square
because it is x^2 and all three numbers are positive it is gna be
(x+?)(x+?)
now you have to find some when added is equal to 15 and multiplyed to get 36 in this case its 3 and 12
therfore the answer is:-
(x+3)(x+12)
2007-11-18 10:35:40
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answer #8
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answered by wag1 2
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at first verify out the numbers : 5 will bypass into the two 15 and 20 so which you would be able to take 5 out as a consumer-friendly ingredient. Then verify out the t's: t^2 will bypass into the two t^2 and t^3 so returned that's taken out as a consumer-friendly ingredient. This leaves 5t^2 exterior the brackets 5t^2(3t - 4) it fairly is 3t-4 in the brackets as 3t x 5t^2 = 15t^3 and four x 5t^2 = 20t^2 desire this permits
2016-12-16 12:35:06
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answer #9
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answered by ? 4
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(x+3)(x+12)=0
2007-11-18 10:33:48
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answer #10
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answered by Anonymous
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