Synthentic Division Simplified

Added: 2026-04-29

[00:00:00]To divide these two polynomials using synthetic division, [music] here are going to be the steps. The first thing, we're going to take our divisor, set it equal to zero, and solve for [music] x.

[00:00:06]In this example, we're going to get the number two. Then, we're going to create a nice box with that two. [music] Then, we're going to take the coefficients of our dividend and go ahead and write them down inside the box. Make sure your dividend is in descending order, meaning highest power first, and there's no missing [music] terms. If you have a missing term, you're going to use zero as your coefficient. In this case, I have a two, -7, >> [music] >> 13, and -14. Now, we just need to apply the synthetic division algorithm. First number is always a freebie.

[00:00:31]>> [music] >> We're going to bring that down. Then, we're going to multiply on the diagonal, add on the vertical. 2 * 2 is 4. -7 + 4 is going to be a -3. [music] -3 * 2 is going to be a -6. 13 + -6 is going to be a -7. -7 * [music] 2 is going to be a positive 14. -14 + 14 is going to be a zero. Now, we need to go ahead and write this [music] as a polynomial. The last number is always going to be your remainder. In this case, you can see it's zero. So, what that tells us is this [music] polynomial evenly divides into that polynomial this polynomial times. But, it's not written as a polynomial yet, [music] right? So, you need to understand this is going to be our constant. This will be the coefficient of our linear term, and this will be the coefficient of our quadratic term. So, to write it as [music] a polynomial, we'll just write 2x squared - a 3x - a 7.