# tricky remainder of the polynomial

• Dec 22nd 2012, 06:08 AM
rcs
tricky 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 AM
jakncoke
Re: 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 AM
rcs
Re: tricky remainder of the polynomial
Quote:

Originally Posted by jakncoke
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 \$

if that is what im going to do, then

[5(-2) + 10]^2012 + 4
[-10 + 10]^2012 + 4
0 + 4
meaning 4 is the remainder

is this correct sir?
• Dec 22nd 2012, 07:41 AM
ILikeSerena
Re: 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 AM
rcs
Re: tricky remainder of the polynomial
Quote:

Originally Posted by ILikeSerena
Did you know that (5x+10)=5(x+2)?

i know above, but below , well i cant, Can you?

Can you rewrite ((5(x+2))^2012)+ 4?

so that it makes things easier now.

thanks
• Dec 22nd 2012, 08:06 AM
jakncoke
Re: tricky remainder of the polynomial
Yes remainder is 4.