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

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- Sep 9th 2012, 01:47 AMrcsquotient of polynomial
when ax^ - 4x + 4 is divided by x - 2, the remainder is 4, what is the quotient?

- Sep 9th 2012, 02:23 AMkalyanramRe: quotient of polynomial
The exponent of x in the first term is missing but here is the general procedure.

We have $\displaystyle ax^\alpha - 4x + 4 = P(x)(x-2)+4$, where $\displaystyle P(x)$ is a polynomial of degree $\displaystyle \alpha-1$

$\displaystyle \implies (ax^\alpha - 4x + 4) - 4 = P(x)(x-2) \implies ax^\alpha - 4x = P(x)(x-2) \implies $ 2 is a root of $\displaystyle ax^\alpha - 4x$ $\displaystyle \implies a2^\alpha = 8 \implies a = \frac{8}{2^\alpha}$ - Sep 9th 2012, 04:15 AMrcsRe: 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 AMskeeterRe: quotient of polynomial
- Sep 9th 2012, 06:03 AMrcsRe: quotient of polynomial
it is impossible because the numerical coefficient in first term is variable a

- Sep 9th 2012, 06:20 AMskeeterRe: quotient of polynomial
is that so?

Code:`2] a ..... -4 ...... 4`

.............2a ....(4a-8)

--------------------------

.....a....(2a-4) ...(4a-4)

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