When Should Synthetic Division Be Used?

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.

When can we not use synthetic division?

We can only divide by a binomial whose leading coefficient is 1–thus, we must factor the leading coefficient out of the binomial and divide by the leading coefficient separately. Also, the

binomial must have degree 1

; we cannot use synthetic division to divide by a binomial like x

²

+ 1.

When can I use synthetic division?

You can use synthetic division

whenever you need to divide a polynomial function by a binomial of the form x – c

. We can use this to find several things. One is the actual quotient and remainder you get when you divide the polynomial function by x – c.

What are the requirements for synthetic division?

• The divisor should be a linear factor. This means that the divisor should be an expression of degree 1.
• The leading coefficient of the divisor should also be 1. If the divisor’s coefficient is other than 1, the synthetic division process will get messed up.

Can you always use synthetic division to divide two polynomials if not when can’t you use synthetic division?

Synthetic division is a shorthand, or shortcut, method of polynomial division in the special case of dividing by a linear factor — and it only works in this case. Synthetic division is generally used, however,

not for dividing out factors but for finding zeroes

(or roots) of polynomials. More about this later.

How do you know what to divide by in synthetic division?

1. Step 1: Set up the synthetic division. …
2. Step 2: Bring down the leading coefficient to the bottom row.
3. Step 3: Multiply c by the value just written on the bottom row. …
4. Step 4: Add the column created in step 3.

What is the formula of synthetic division?

Synthetic division is a shorthand method of dividing polynomials for the special case of dividing by a linear factor whose leading coefficient is 1. …

Divide 2×3−3×2+4x+5 2 x 3 − 3 x 2 + 4 x + 5 by x+2

using the long division algorithm.

Do you add or subtract in synthetic division?

If a term is missing, add it in with a coefficient of 0. Step 2: Set the denominator equal to 0 and solve to find the number to put as the divisor. When you use long division, you subtract at each step.

Synthetic division uses addition instead

, so we switch the sign to account for this.

What if there is a remainder in synthetic division?

The remainder in synthetic division could be written

as a fraction or with R written in front of it

. If writing as a fraction, the remainder is in the numerator of the fraction and the divisor is in the denominator. For example: … When you use Synthetic Division, the answer is x+6 with a remainder of 6.

How do you use synthetic division to find a function value?

1. Write only the coefficients of x in the dividend inside an upside-down division symbol. …
2. Put the divisor at the left. …
3. Drop the first coefficient of the dividend below the division symbol. …
4. Multiply the drop-down by the divisor, and put the result in the next column. …
5. Add down the column.

What is the quotient in synthetic division?

Synthetic Division by x − a. 5 is called the divisor, 47 is the dividend,

9

is the quotient, and 2 is the remainder. Or, Dividend = Quotient· Divisor + Remainder.

Can I use synthetic division instead of long division?

Polynomial synthetic division is a simplified form of polynomial division that is used only in

the case of division by a linear factor

, a monomial. … It does away with division brackets and variables used in polynomial long division and focuses on the coefficients of the polynomial in question.