# Math Help - quotient of polynomial

1. ## quotient of polynomial

when ax^ - 4x + 4 is divided by x - 2, the remainder is 4, what is the quotient?

2. ## Re: quotient of polynomial

The exponent of x in the first term is missing but here is the general procedure.

We have $ax^\alpha - 4x + 4 = P(x)(x-2)+4$, where $P(x)$ is a polynomial of degree $\alpha-1$
$\implies (ax^\alpha - 4x + 4) - 4 = P(x)(x-2) \implies ax^\alpha - 4x = P(x)(x-2) \implies$ 2 is a root of $ax^\alpha - 4x$ $\implies a2^\alpha = 8 \implies a = \frac{8}{2^\alpha}$

3. ## Re: quotient of polynomial

when ax^2 - 4x + 4 is divided by x - 2, the remainder is 4, what is the quotient? sorry this should have been the correct one...

4. ## Re: quotient of polynomial

Originally Posted by rcs
when ax^2 - 4x + 4 is divided by x - 2, the remainder is 4, what is the quotient? sorry this should have been the correct one...
perform synthetic division

5. ## Re: quotient of polynomial

it is impossible because the numerical coefficient in first term is variable a

6. ## Re: quotient of polynomial

Originally Posted by rcs
it is impossible because the numerical coefficient in first term is variable a
is that so?

Code:
2]   a ..... -4 ...... 4
.............2a ....(4a-8)
--------------------------
.....a....(2a-4) ...(4a-4)
$4a-4$ is the remainder ... set that equal to 4 and solve for $a$

... note you could also use the remainder theorem to answer this question.