1. ## Polynomial division

Question 43 and 44

Sent from my iPad using Tapatalk

2. ## Re: Help #3

Please show what you have tried. It will be much easier to help you if we know where you are stuck and why. Here is a hint for #43. Show your work for #44 and we can help from there.

Suppose the function is $f(x)$. Then

$f(x) = (x+1)p_1(x)$

$f(x) = (3x-1)p_2(x)+4$

$f(x) = (3x^2+2x-1)p_3(x) + hx+k$

Find $f(x)$ when $x+1=0$ and when $3x-1=0$. Then plug that into the third equation and you will get a system of equations that will allow you to solve for $h,k$

3. ## Re: Help #3

Originally Posted by SlipEternal
Please show what you have tried. It will be much easier to help you if we know where you are stuck and why. Here is a hint for #43. Show your work for #44 and we can help from there.

Suppose the function is $f(x)$. Then

$f(x) = (x+1)p_1(x)$

$f(x) = (3x-1)p_2(x)+4$

$f(x) = (3x^2+2x-1)p_3(x) + hx+k$

Find $f(x)$ when $x+1=0$ and when $3x-1=0$. Then plug that into the third equation and you will get a system of equations that will allow you to solve for $h,k$
When g(x) is divided by x-3 the rem in 3 right,then f(x) is divided by x-3 rem is 57.so what next?should i combine these

Sent from my iPad using Tapatalk

4. ## Re: Polynomial division

Write $g(x)+3=(x-3)p(x)$

Then $g(x)=(x-3)p(x)-3$

Plug in:

$f(x)=(x^4-x^3+2x-3)((x-3)p(x)-3)$

Multiply out.

$f(x)=(x^4-x^3+2x-3)(x-3)p(x)-3(x^4-x^3+2x-3)$

The first term is divisible by $x-3$. So use long division on

$\dfrac{-3x^4+3x^3+0x^2-6x+9}{x-3}$