Synthetic division

Synthetic Division,[object Object],By: Alyssa Barnett,[object Object]

Synthetic Division,[object Object],Synthetic division is a method of long division, but only using less writing and not as much solving. ,[object Object],a method of dividing polynomials in which you leave out all variables and exponents and perform division on the list of coefficients. You also switch the sign of the divisor so that you can add throughout the process,[object Object]

Steps to Solving,[object Object],1. Write the coefficients down in order,[object Object],2. Draw a box and line, then switch the sign of what you are dividing by,[object Object],3. Drop the first number down. That number stays the same,[object Object],4. From then on out, multiply by the divisor, add numbers, then repeat for the rest of the problem,[object Object]

Examples,[object Object],(3x^3 + 7x^2 – 9x + 12) / (x + 4),[object Object],In this problem you have 4 numbers to bring down. So start off by drawing a line then bringing down only the numbers.,[object Object], 3 7 -9 12,[object Object],_______________________,[object Object]

Example cont…,[object Object], 3 7 -9 12,[object Object], _______________________,[object Object],In a little box near the three write the number that is the divisor. Which is the four. But, in synthetic you switch the sign. This will make the divisor now -4. ,[object Object],Always in a synthetic equation you bring down the very first coefficient. The three will come down and then you start multiplying and adding. ,[object Object]

Example cont…,[object Object], /-4/ 3 7 -9 12,[object Object], _______________________,[object Object], 3 ,[object Object],Start multiplying and adding. ,[object Object],-4 * 3 = -12 ; You now put the -12 under the 7 because you are going to add those numbers. ,[object Object],-12 + 7= -5; You write the -5 under the line where you added them,[object Object],Now, multiply the -4 and -5, then add,[object Object]

/-4/ 3 7 -9 12,[object Object],_______-12___ 20__ -44___,[object Object],3 -5 11 -32,[object Object],The problem is finished except you have a remainder. The way to know if you have a remainder is if the very last numbers you add up together don’t cancel each other out.,[object Object]

Remainder,[object Object],The remainder in Synthetic Division problems is always based on the very last numbers you add up together. So, for the example we did, there was a remainder of -32. Adding 12 and -44 didn’t cancel out or equal zero. ,[object Object],When writing the finishing problem, your numbers left under the line are what you will use. 3, -5, 11, and -32. ,[object Object],Whatever number of (x) you used in the original problem, you use one less in the finishing problem. So, when the original problem starts off with 3x^3, you will end up with 3x^2 and keep going down until you have no more x’s.,[object Object]

Synthetic Division,[object Object],The finishing problem will look like this…,[object Object],3x^2 – 5x + 11 + -32/x + 4,[object Object],The remainder of the problem is added in the equation. The remainder on top and the original divisor equation, which was (x + 4), goes on the bottom.,[object Object]

Synthetic division

Synthetic division

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Synthetic division