Question

X-3÷4x^4-8x^3-18x^2+17x+3​

Answer 1

The simplication of x-3÷4x^4-8x^3-18x^2+17x+3 is
`(1)/(\left(4 x^(3)+4 x^(2)-6 x-1\right))`

Solution:

`\text { Given, expression is }(x-3) /\left(4 x^(4)-8 x^(3)-18 x^(2)+17 x+3\right)`

Now we have to simplify the given expression,

For that, we have to factorize the denominator.

`\text { So, } 4 x^(4)-8 x^(3)-18 x^(2)+17 x+3`

`\Rightarrow 4 x^(4)+\left(-12 x^(3)+4 x^(3)\right)+\left(-12 x^(2)-6 x^(2)\right)+(18 x-x)+3`

By grouping terms we get,

`\rightarrow\left(4 x^(4)-12 x^(3)\right)+\left(4 x^(3)-12 x^(2)\right)-\left(6 x^(2)-18 x\right)-(x-3)`

By taking the common terms,

`\begin{array}{l}{\rightarrow 4 x^(3)(x-3)+4 x^(2)(x-3)-6 x(x-3)-(x-3)} \\\\ {\rightarrow(x-3)\left(4 x^(3)+4 x^(2)-6 x-1\right)}\end{array}`

`\begin{array}{l}{\text { Now, }(x-3) /\left(4 x^(4)-8 x^(3)-18 x^(2)+17 x+3\right) \rightarrow (x-3)/(\left(4 x^(4)-8 x^(3)-18 x^(2)+17 x+3\right))} \\\\ {\quad \rightarrow (x-3)/((x-3)\left(4 x^(3)+4 x^(2)-6 x-1\right))} \\\\ {\quad \rightarrow (1)/(\left(4 x^(3)+4 x^(2)-6 x-1\right))}\end{array}`

Hence, the simplified expression is
`(1)/(\left(4 x^(3)+4 x^(2)-6 x-1\right))`