Question

how do you use synthetic division

Answer 1

Hey, buddy. c:

Answer 2

hi there

Answer 3

First, let's start with the "When can I use it?"

Answer 4

Using synthetic division, what is the quotient: (y^3 - 8y^2 - 3y + 54) ÷ (y - 3) ?

Answer 5

You can use synthetic division to divide a polynomial by a binomial, that means the thing you're dividing by only has 2 terms. So, things like (x+1), (x-3), (x+9)
but not things like (3x^2+x+9) because that has 3 terms.

Answer 6

Cool so far? 2 terms only.
The other requirement is that the x term has to have no coefficient and no power.
So I can use synthetic if I'm dividing by
(x+9)
but not if I'm dividing by
(2x+9)
and not if I'm dividing by
(x^2+9)

Answer 7

Does that make sense?

Answer 8

yes it makes sense.

Answer 9

Great. So, we have a division problem, and we've checked that it's something we're allowed to do synthetic division for. Here's how we set the problem up. Draw yourself a line like this:

Answer 10

ok

Answer 11

On the inside, we're going to put the thing we're dividing INTO, but we only put the coefficients. It seems super simple, and it is, but there are a couple of tricks you have to know.
If there is no coefficient written, then the coefficient is 1, so that's what we'll write.
If there is a term MISSING, like, it skips from 4x^4 to x^2 without an x^3 term, then we need to write a 0 in that spot, as in "0x^3".

So here's an example. If I was doing this division problem
\[(6x^5 + x^4 -x^2 +10) \div (x+7)\]
I would fill in the inside like this: