Question 43 and 44

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- Jul 12th 2018, 07:17 AM #1

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- Jul 12th 2018, 08:32 AM #2

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## 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 $h,k$

- Jul 12th 2018, 04:36 PM #3

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- Jul 12th 2018, 05:33 PM #4

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## 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

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