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- 1. Maths – Core 2 – Algebraic Division (and Remainder theorem)
- 2. I bet all of you lot forgot how to do long division, SO I’m gonna remind you how…. E.G - 145,650 ÷4 So we write it out like this 4 145, 650 So we have 4, and we want to see how many 4 145, 650 of those can fit into 145,650 We split the large number 4 14-56-50 into smaller ones which we can easily use so we can divide much more easily.
- 3. each time we go down we’re going to split the numbers again differently. You’ll see why :P 36412.5 4 14-56-50 -12 025-65-0 So 4*6 = 24, the 24 is taken away from 25 giving -24 us 1 and the 6 goes on top So now that we have 50 16-50 The 16 is completely left on it’s own, we can -16 divisible by 4 so it goes on top but we have nothing divide it by 4, which will give us 12.5, which can 00-50 left so we move over to the 50 now be added on to the top and our answer is complete
- 4. Algebraic Division, works pretty much in the same way…. E.G 4x³ + 2x²+ 3x + 5 ÷ (x +2) Set it out the same way (x+2) 4x³ + 2x²+ 3x + 5 AND SOLVE BITCH SOLVE (just kidding I’ll show you how :P)
- 5. So ignoring the +2 (because it will sort itself out) We need to know how many -25 times x can go into 4x³, which is 4x² etc… 4x²-6x+15x+(x+2) we then 1. Add that to the top as (x+2) 4x³+2x²+3x+5 part of out answer 4x² (x+2) -(4x³+8x²) 2. Times it by (x+2) 3. Take away the expanded brackets 0+(-6x²+3x) 4. Repeat process for the next few.. -6x (x+2) -(-6x²-12x) Just like normal division Note: If the trinomial has a 0+15x+5 part of the sentence not included, you should add the 15x (x+2) -(15x + 30) omitted part e.g 4x³ + 2x²+ 5 ÷ (x +2) 0 -25 When you go to solve it, it should be written as…. Woah, what’s this? We have a (x+2) 4x³ + 2x²+ 0x + 5 remainder????, Yes we take it to the top This will make solving it much and divide it by (x+2) and add it on easier
- 6. Remainder Theorem This is basically a way of finding out the remainder, MUCH FASTER!!! When we have to divide 4x³ + 2x²+ 3x + 5 by (x+2). But they only want the value of the remainder, there are much quicker ways of going about this. Well there’s this little saying, (To be honest with When f(x) divides by (ax+b) you, I have no idea The remainder is -b what that means :L) f a But in essence, what you do is, you get b and (x+2) = (ax+b) substitute –b into x into the trinomial So –b= -2 4x³ + 2x²+ 3x + 5 Use a becomes calculator, it 4*(-2)³+2*(-2)²+ (3*-2)+5 really helps :P And then Solve!!, so 4*(-2)³+2*(-2)²+ (3*-2)+5 = -25 -25, as you know so well, was the remainder in the previous example (just to show you it works)