2x2 = 10x + 12 2x2 - 10x - 12 = 0 x2 -5x -6 = 0 x2 - 6x + x - 6 = 0 x(x -6) + 1(x -6) = 0 (x+1)(x-6) = 0 x = -1 or x = 6
2X2+5x-12 4+5x-12 -8+5x 5x-8
2x2 + 10x + 25 is a quadratic expression. It describes a parabola.
x2+10x-24 = (x-2)(x+12)
The GCF of 4 and 12 is 4.
Doesn't factor evenly, use quadratic
2x2 = 10x + 12 2x2 - 10x - 12 = 0 x2 -5x -6 = 0 x2 - 6x + x - 6 = 0 x(x -6) + 1(x -6) = 0 (x+1)(x-6) = 0 x = -1 or x = 6
2x2 - 5x + 12 does not factor. 2x2 - 5x - 12 factors into (2x + 3)(x - 4) 2x2 + 5x - 12 factors into (2x - 3)(x + 4)
20x3 - 70x2 + 60x = 10x(2x2 - 7x + 6) = 10x(2x - 3)(x - 2).
2X2+5x-12 4+5x-12 -8+5x 5x-8
2x2 + 10x + 25 is a quadratic expression. It describes a parabola.
(x + 2)(x - 12)
x2+10x-24 = (x-2)(x+12)
(2x - 3)(x - 12)
The GCF of 4 and 12 is 4.
2x2 - 72 would be factored into (2x - 12)(x + 6) or (2x + 12)(x - 6) To double check, multiply each pair: (2x - 12)(x + 6) = 2x2 + 12x - 12x - 72 = 2x2 - 72 (2x + 12)(x - 6) = 2x2 - 12x + 12 x - 72 = 2x2 - 72
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)