How To Divide Polynomials Using Synthetic Division

As purple math nicely states synthetic division is method for dividing by a linear factor meaning the polynomial on the bottom is of degree 1 and shortens the process of dividing polynomials because there is less writing and calculations involved due to the fact that we are only going to be focusing on the coefficients rather than the variables and exponents.

In general you can skip the multiplication sign so 5 x is equivalent to 5 x. Our first step is to list the coefficients of the polynomials in descending order and carry down the first coefficient. Bring the lead coefficient down. If you are dividing by a longer polynomial say x2 2 x 5.

Add the terms of the second column. Write the product in the next column. Synthetic division is a shorthand method of dividing polynomials where you divide the coefficients of the polynomials removing the variables and exponents. This video shows through an example of how to divide a polynomial by a trinomial using synthetic division to see an example of using synthetic division to di.

Write the coefficients of the dividend. In general you can skip parentheses but be very careful. We find the sum of this number with the next coefficient and place the sum below the line. Multiply the lead coefficient by k.

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It allows you to add throughout the process instead of subtract as you would do in traditional long division. Write the product in the next column. Remember to place a when there isn t a coefficient given. We multiply what s below the line by and place the product on top of the line.

The calculator will divide the polynomial by the binomial using synthetic division with steps shown. Given two polynomials use synthetic division to divide. Write k for the divisor. The basic mantra to perform the synthetic division process is bring down multiply and add multiply and add multiply and add for example we can use synthetic division method to divide a polynomial of 2 degrees by x a or x a but you cannot use this method to divide by x 2 3 or 5x 2 x 7.