When factoring what do you do when it is impossible to get a number that multiplies or adds properly?
962639
You write that it cannot be factored.
441409
Do the multiplication as if the decimal point wasn't there.  In this case, the problem becomes 69 times 38, and your answer would be 2622.\n\nThen, when you're done, count the number of decimal places after the point, in both of the numbers you're multiplying.  In this case, it would be one - the 8 in 3.8.\n\nThen count that same number of spaces from the end in your answer, and add the decimal point in that spot.  That would change your answer to 262.2.\n\nHere's another example:\n9.7 times 4.3\nChange it to 97 times 43\nThe result is 4171\nCount the numbers after the decimals - this time it's two - the 7 in 9.7, and the 3 in 4.3\nCounting back two from the end of 4171 gets us an answer of 41.71
934652
So let's say the problem looks like this\n\n   11\nx 12\n--------\n        <-----the answer from 11*2\n       <------answer from 11*1\n\nfirst hide the 1 from the 12 and work out the problem as 11*2\nthen work on multiplying the 1 with 11 but make sure you start putting your answer down below your first answer and the answer starts in the column that is below the 1 from the 12.\n\nfinally when the two answers are found, you can add them and get your final answer. SOOO here's what it looks like\n\n      11\n   x  12\n--------------\n           22    (this is from 11x2)\n +  11       (this is from 11 x1)\n------------\n     132 = final answer!
832637
your question does not make sense, the numbers are impossible
859462
I see your preferred method is ask it here and have someone else figure it out for you...\n\nI think you'll learn more if you try them yourself.\n\nFor the addition and subtraction I would write them as numbers on top of each other and use carrying and borrowing rules:\n\n176\n+43\n-----\n\n.492\n-273\n------\n\nFor the multiplication, you would again put them on top of each other and multiply a digit at a time, then add the results.\n\n136\nx21\n------\n..136\n272\n-------\n\nFor the division, I would suggest long division\n.. _____\n3 ) 429
805233
Can you factor the numerator?\n\nI guess not, but UMR math major ignores your denominator in the original problem.
464534
Actually, -18 *does* have something to do with it. Try to find two numbers which multiply to give -18 and which add to give -5. In this case, it doesn't work, so the polynomial doesn't factor.\n\nConsider 8x^2-10x-3. Multiply the 8 and -3 to get\n-24. Now find to numbers which multiply to give -24 and which add to give -10. In this case -12 and 2 work. Now do this:\n\n8x^2-10x-3=\n8x^2-12x+2x-3= (using the -12+2=-10)\n4x(2x-3)+(2x-3)= (factoring 1st two and last two terms)\n(4x+1)(2x-3).\n\nThis gives a better way to factor that simple guessing. It will always work if the quadratic can be factored.
890645
Wow, there is a lot here!  I'll start with some tips for solving algebra problems.  The first thing you should always remember is to play the equal game.  Whenever you add, subtract, multiply, or divide, you should do the same to the other side.  The other tip is to use the order of operations when simplifying.  Remember the sentence: Please excuse my dear Aunt Sally.  The initial letters of each word stands for the order of operations.  Do the Parenthesis first, followed by the Exponents, then Multiplication or Division, and Addition and/or subtraction next.  Finally, you should always simplify first using the order of operations before you start shifting numbers from one side of the = to the other.  \n\nI'm not going to work all of these problems, but I'll show you a few to get you started.\n\n1)\n3x-7 = 2   Add 7 to both sides\n3x = 9   Divide by 3\nx = 3\n\n4)\n6x - 3 = 2x - (4-3)/3   Simplify the stuff inside the parenthesis first\n6x - 3 = 2x - 1/3  Add 3 to both sides\n6x = 2x - 5/3  Subtract 2x from both sides\n4x = -5/3  Multiply both sides by 3\n12x = -5  Divide both sides by 12\nx = -12/5\n\nI hope this helps.  Good luck!
302292
There's no solution.\n\nIf you're evil, you could argue that 102 - 78 is an answer ;)\n\nEDIT : Confirmed no solution with Telraam (http://members.chello.nl/g.de.blaauw/telraam.html). Allowing square roots gives (8*(2+.10))/.7 as a potential answer.
903533
ignore the decimals when u originally do the problem, then however many deciams there are in both of the decimals you're multiplying is how many there will b in the answer. i.e. if you multiply 6.78x4.234 together the answer will have 5 numbers behidnthe dceimal point
681272
If decimals are allowed, then (73+7)*.3 is a nice solution :)\n\nIf not, then the only solution I could find is (3+(3/7))*7\n\nEDIT : As for the initial question, absolutely! Math is my favorite subject, even in college. I won several contests in high-school, and love any sort of math puzzles. If you know of any more, please e-mail me :)\n\nSubmarinerdave : Heh. That's what I thought of as well, my sister has a 24 contest at her school two years ago :) A similar but more challenging game is the 2006 math game, where you try to make numbers from 1 to 100 using the digits 2,0,0, and 6. Link below.
437150
The big rule to follow is that you have two quantities that are equal, and you do the same thing to both of them, what you get will be equal.\n\nSo you can add, subtract, multiply, and divide both sides of an equation by the same thing and the equation remains valid.\nNote: You can't multiply or divide by 0.\n\nThe idea is to pick what you add, subtract, etc. by so that you end up with something simpler than what you started with. You want to add and subtract things that will make pieces of the equation disappear.\n\nIn your case, if you subtract 3x from both sides to get rid of one term from the left side. You  end up with 7 = x.\n\nIf you had something like 6x + 2  = 3x + 5\n\nFirst you subtract 3x from both sides to get \n3x + 2  =  5\n\nThen you subract 2 from both sides to get\n3x = 3\n\nThen you divide both sides by 3 to get\nx = 1.\n\nThen you substitute 1 for x in the orginal equation to check you work.\n\nAgain, at each step, try to do one thing to make things simpler. Do the same thing to both side of the equation.
503153
(x+7)(x+3)\n(x-11)(x+2)\nforget this one.  its AC factoring though\nthis ones AC too
188047
you cannot factor this using integers or rational numbers.
1081089
[ (50000 x 2.4)+(25000 x .8) ] / (50000+250000)=1.8\n\nThe remainder of the info in the problem is not necessary.
803895
To factor a number means to break it up into numbers that can be multiplied together to get the original number.
713027
Just try out small numbers. 1, 2, 3, 4, 6, 8 all work. Once you start doing anything higher, the second factor becomes smaller again, so the others are 96/8, 96/6, 96/4, 96/3, 96/2, 96/1.\nIn all: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96.