Can we use synthetic division to divide a polynomial $p(x)$ by $ax - k$ where $a \ne 1$?

For example:
$(6x^2 - 18x - 3) \div (4x - 3)$

Question

Can we use synthetic division to divide a polynomial $p(x)$ by $ax - k$ where $a \ne 1$?

For example:
$(6x^2 - 18x - 3) \div (4x - 3)$

parthkohli · Answer

I need a yes/no. And this is not homework(school math is easy)

compassionate · Answer

(a +a^x-a)/(a+2) <== Does it follow this format?

compassionate · Answer

Pardon me if I'm wrong, but no, you can't use that because it needs to follow a polynomial form.

parthkohli · Answer

No, it doesn't. $x $ in the divisor has a coefficient which is not 1.

parthkohli · Answer

@across

compassionate · Answer

It looks like you have a quadratic trinomial over (4x - 3)

Synthetic division works with polynomials.

parthkohli · Answer

If so, then can you give me an example by doing the question I gave above?

anonymous · Answer

You can't use synthetic division when the divisor has a leading coefficient other than 1.

parthkohli · Answer

You can't? Woohoo!

compassionate · Answer

$$a \neq 1$$

I looked right over that.

anonymous · Answer

lol. Yeah it's one of the conditions to use it :D

parthkohli · Answer

Haha okay