applying the remainder and factor theorems to divide

[Greta]

Can I use synthetic division to solve this or do I have to use long division?

( 4 x[sup:280lbqti]4[/sup:280lbqti] - 17 x[sup:280lbqti]2[/sup:280lbqti] + 9x - 18) / (2x[sup:280lbqti]2[/sup:280lbqti] - 2)

If I can use synthetic division, is k=2?

 

[soroban]

Hello, Greta!

Can I use synthetic division to solve this or do I have to use long division?

. . \(\displaystyle \dfrac{4x^4 - 17x^2 + 9x - 18}{2x^2-2}\)

Long division is safer . . . but it is still tricky.


\(\displaystyle \begin{array}{cccccccccccc} &&&&&& 2x^2 &&& - & \frac{13}{2} \\ && -- & -- & -- & -- & -- & -- & -- & -- & -- \\ 2x^2-2 & | & 4x^4 &&& - & 17x^2 & + & 9x & - & 18 \\ && 4x^4 &&& - & 4x^2 \\ && -- & -- & -- & -- & -- \\ &&&&& - & 13x^2 & + & 9x & - & 18 \\ &&&&& - & 13x^2 &&& + & 13 \\ &&&&& -- & -- & -- & -- & -- & -- \\ &&&&&&&& 9x & - & 31 \end{array}\)

 

[Greta]

Thank you!!!