My personal tastes are not to like synthetic division because it is very, very, very algorithmic. I prefer to do traditional algebraic long division. But I think you'll see that this has some advantages. It can be faster. And it also uses a lot less space on your paper. So let's actually perform this synthetic division. Let's actually simplify this expression. Before we start, there's two important things to keep in mind. We're doing, kind of, the most basic form of synthetic division.
And to do this most basic algorithm, this most basic process, you have to look for two things in this bottom expression. The first is that it has to be a polynomial of degree 1. So you have just an x here.
You don't have an x squared, an x to the third, an x to the fourth or anything like that. The other thing is, is that the coefficient here is a 1. There are ways to do it if the coefficient was different, but then our synthetic division, we'll have to add a little bit of bells and whistles to it.
So in general, what I'm going to show you now will work if you have something of the form x plus or minus something else. So with that said, let's actually perform the synthetic division. So the first thing I'm going to do is write all the coefficients for this polynomial that's in the numerator.
So let's write all of them. So we have a 3. We have a 4, that's a positive 4. Long division is useful with the remainder and factor theorems, but long division can be time consuming. To divide a polynomial by a binomial and compute the remainder, we can also use synthetic division. We can only divide by a binomial whose leading coefficient is thus, we must factor the leading coefficient out of the binomial and divide by the leading coefficient separately.
Here are the steps for dividing a polynomial by a binomial using synthetic division: Write the polynomial in descending order, adding "zero terms" if an exponent term is skipped. It is an alternative to the traditional long division method used to solve the polynomial division. We can perform synthetic division using some general steps.
Take the coefficients alone, bring the first down, multiply with the zero of the linear factor, and add with the next coefficient and repeat until the end. Synthetic division can be generalized and expanded to the division of any polynomial with any polynomial.
It is an easier method in comparison to the long division method for performing division on polynomials with the linear divisor. This method uses fewer calculations and is quicker than long division.
It takes comparatively lesser space while computing the steps involved in the polynomial division. The synthetic division can be used only when the divisor is a linear polynomial. We have to follow the long division method for the other cases. Synthetic division of polynomials helps in finding the zeros of the polynomial. It also reduces the complexity of the expression while dividing the polynomials by a linear factor. In synthetic division, the polynomial obtained is one power lesser than the power of the dividend polynomial.
The result obtained can be arranged to form the quotient of the polynomial division. Learn Practice Download. Synthetic division is another way to divide a polynomial by the binomial x - c , where c is a constant. Step 1: Set up the synthetic division. Step 2: Bring down the leading coefficient to the bottom row. Step 3: Multiply c by the value just written on the bottom row.
Step 4: Add the column created in step 3. Synthetic division is a shortcut that can be used when the divisor is a binomial in the form x — k. In synthetic division , only the coefficients are used in the division process. Synthetic Division. Synthetic division is another method of dividing polynomials. It is a shorthand of long division that only works when you are dividing by a polynomial of degree 1. Asked by: Lhoucine Astica asked in category: General Last Updated: 12th March, Can you always use synthetic division when dividing polynomials?
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