quotient of polynomial

• Sep 9th 2012, 01:47 AM
rcs
quotient of polynomial
when ax^ - 4x + 4 is divided by x - 2, the remainder is 4, what is the quotient?
• Sep 9th 2012, 02:23 AM
kalyanram
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 $ax^\alpha - 4x$ $\implies a2^\alpha = 8 \implies a = \frac{8}{2^\alpha}$
• Sep 9th 2012, 04:15 AM
rcs
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...
• Sep 9th 2012, 06:01 AM
skeeter
Re: quotient of polynomial
Quote:

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
• Sep 9th 2012, 06:03 AM
rcs
Re: quotient of polynomial
it is impossible because the numerical coefficient in first term is variable a
• Sep 9th 2012, 06:20 AM
skeeter
Re: quotient of polynomial
Quote:

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.