d/dx 2x2+3x+7=4x+3
2x2 + 21x + 49 = 2x2 +14x +7x + 49 = 2x(x + 7) + 7(x + 7) = (2x + 7)(x + 7)
2x2 + 5x - 3 (2x - 1)(x + 3)
If it a 2x2 matrix, the determinant is 3*a - (-2)*5 = 3a + 10 = 7 So 3a = -3 so a = -1
(x3 + 3x2 - 2x + 7)/(x + 1) = x2 + 2x - 4 + 11/(x + 1)(multiply x + 1 by x2, and subtract the product from the dividend)1. x2(x + 1) = x3 + x22. (x3 + 3x2 - 2x + 7) - (x3 + x2) = x3 + 3x2 - 2x + 7 - x3 - x2 = 2x2 - 2x + 7(multiply x + 1 by 2x, and subtract the product from 2x2 - 2x + 7)1. 2x(x + 1) = 2x2 + 2x2. (2x2 - 2x + 7) - (2x2 + 2x) = 2x2 - 2x + 7 - 2x2 - 2x = -4x + 7(multiply x + 1 by -4, and subtract the product from -4x + 7)1. -4(x + 1) = -4x - 42. -4x + 7 - (-4x - 4) = -4x + 7 + 4x + 4 = 11(remainder)
d/dx 2x2+3x+7=4x+3
See http://www.wolframalpha.com/input/?i=integrate+2exp(-x2)+over+3+to+7
∫(4x3 - 2x2 + x - 1) dx You can integrate this by taking the antiderivative of each term. Each of these terms is in the format axn, the antiderivative of which is axn-1/n: = ∫(4x3)dx - ∫(2x2)dx + ∫(x)dx - ∫(1)dx = x4 - 2x3/3 + x2/2 - x + C
2x2 - 13x - 7 = (2x + 1)(x - 7)
2x2 equals 5
2x2 + 21x + 49 = 2x2 +14x +7x + 49 = 2x(x + 7) + 7(x + 7) = (2x + 7)(x + 7)
2x2 - x = 21Subtract 21 from each side . . 2x2 - x - 21 = 0Factor the left side . . . . . . . . (2x - 7) ( x + 3) = 0If (2x - 7 = 0), then . . . . . x = 3.5If (x + 3 = 0), then . . . . . x = - 3
2x2 + 5x - 3 (2x - 1)(x + 3)
588 4 x 147 (2x2) x (3x49) (2x2) x (3 x (7x7)) Since 2, 3, and 7 are prime numbers, the factor tree is complete.
7 1/4 + 3 1/2= 7 1/4 + 3 1x2/2x2= 7 1/4 + 3 2/4= 10 3/4
2x2+10x+12/(x+3)We use long division just like we would normally.Let me give you an example.ex:Divide 7 into 23---------7 | 234We say ok, how many times does 7 go into 2?0 times, it doesn't work. So you put a 0 above the 2.Now we try 7 into 23. It can go 3 times, so we put a 3 above the 3 (in 234) and subtract 21. (3 *7) and then carry down the 4....03--------7|234-..21--------...024how many times will 7 go into 24? 3 again....033-------7|234-..21-------...024-....21--------.......3We're left with 3 as the remainder.Our answer to 234 divided by 7 is 33 remainder of 3, or 33 and 3/7.----This method works similarly with variables.2x2+10x+12/(x+3)----------------------x+3|2x2+10x+12We'll start the same way. How many times will X go into 2x2Or, what times X gives 2x2 x * 2x = 2x2So we write a 2x above the 2x2, just like we wrote the 3 in the example above........2x----------------------x+3|2x2+10x+12Now we multiply x+3 by 2x to figure out what to subtract.2x(x+3)= 2x2 +6xNotice we ended up with a 2x2? This is what we wanted to subtract! Something to note, when you do your subtraction, you're subtracting the entire expression 2x2 +6x.So you can write -2x2 - 6x........2x----------------------x+3|2x2+10x+12......-2x2 - 6x-----------------...............4x + 12Make sure you carry down the next term, the +12. Just like we carried down the 4 in the example above.Now, how many times will X go into 4x? 4 times. So we write a 4 next to the 2x.and then multiply 4(x+3). then subtract........2x + 4----------------------x+3|2x2+10x+12......-2x2 - 6x-----------------...............4x + 12..............-4x - 12---------------------........................0In this scenario we get a remainder of 0.This means that x+3 divides evenly into 2x2+10x+12.In fact, it can divide into it 2x +4 times.To check this, multiply (x+3)(2x+4) use FOIL.(x+3)(2x+4) = 2x2+10x+12 (check)Side note: If you did get a remainder, like in the 1st example. Let's say the remainder was 1.You take the remainder, 1 and put it over the divisor x +3.so your answer would be 2x+4 +(1/x+3)
2x2 - 3 = 13 So 2x2 = 16 x2 = 8 So that x = ±2√2