remainder if ((5x+10)^2012)+ 4 divided by x+2

can anyone help me on this please

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- Dec 22nd 2012, 06:08 AMrcstricky remainder of the polynomial
remainder if ((5x+10)^2012)+ 4 divided by x+2

can anyone help me on this please - Dec 22nd 2012, 07:23 AMjakncokeRe: tricky remainder of the polynomial
Theres a theorem that says that, the remainder of Any polynomial divded by a linear factor, $\displaystyle a_n x^n +...+a_0 $ divided by $\displaystyle x - a $ the remainder is f(a).

For example, $\displaystyle x^3 + x^2 + 3 $ divided by $\displaystyle x+ 3 = x - -3$, the remainder is $\displaystyle f(-3)= (-3)^3 + (-3)^2 + 3 = 21 $ - Dec 22nd 2012, 07:37 AMrcsRe: tricky remainder of the polynomial
- Dec 22nd 2012, 07:41 AMILikeSerenaRe: tricky remainder of the polynomial
Did you know that (5x+10)=5(x+2)?

Can you rewrite ((5(x+2))^2012)+ 4? - Dec 22nd 2012, 07:46 AMrcsRe: tricky remainder of the polynomial
- Dec 22nd 2012, 08:06 AMjakncokeRe: tricky remainder of the polynomial
Yes remainder is 4.