Question

I’ve tried so hard to do this i can’t get it

Answer 1

Answer would be 1x^3 -2x^2+8x-40.

For the solution, we used long division for polynomial.

Refer to the attached pic.

Answer 2

`x^3+\boxed{-2}\:x^2+\boxed{8}\:x+\boxed{-40}`

Explanation:

Given division:

`(x^4+2x^3-8x-160)/(x+4)`

The dividend is the polynomial which has to be divided, and the divisor is the expression by which the dividend is divided.

Therefore, in this case:

`(x^4+2x^3-8x-160)/(x+4)\;\begin{array}{l}\leftarrow \; \sf Dividend\\\leftarrow \; \sf Divisor\end{array}`

Long Division Method of dividing polynomials

• Divide the first term of the dividend by the first term of the divisor and put that in the answer.
• Multiply the divisor by that answer, put that below the dividend and subtract to create a new polynomial.
• Repeat until no more division is possible.

Create the long division by placing the divisor (x + 4) to the left of the dividend (x⁴ + 2x³ - 8x - 160):

`\large \begin{array}{r}\phantom{)}\\x+4{\overline{\smash{\big)}\,x^4+2x^3-8x-160\phantom{)}}\\\end{array}`

Divide the first term of the dividend (x⁴) by the first term of the divisor (x):

`(x^4)/(x)=x^3`

Place x³ in the answer section:

`\large \begin{array}{r}x^3\phantom{wwwwwww)}\\x+4{\overline{\smash{\big)}\,x^4+2x^3-8x-160\phantom{)}}\end{array}`

Multiply the divisor (x + 4) by that answer (x³):

`(x+4) \cdot x^3=x^4+4x^3`

and put that below the dividend. Draw a line under this:

`\large \begin{array}{r}x^3\phantom{wwwwwww)}\\x+4{\overline{\smash{\big)}\,x^4+2x^3-8x-160\phantom{)}}\\{-~\phantom{(}\underline{(x^4+4x^3)\phantom{-bwwww..)}}\end{array}`

Now, subtract (x⁴ + 4x³) from the polynomial above it to create a new polynomial. Place this below the line:

`\large \begin{array}{r}x^3\phantom{wwwwwww)}\\x+4{\overline{\smash{\big)}\,x^4+2x^3-8x-160\phantom{)}}\\{-~\phantom{(}\underline{(x^4+4x^3)\phantom{-bwwww..)}}\\-2x^3-8x-160\phantom{)}\end{array}`

Repeat this process until no more division is possible:

`\large \begin{array}{r}x^3-2x^2+8x-40\phantom{.)}\\x+4{\overline{\smash{\big)}\,x^4+2x^3-8x-160\phantom{)}}\\{-~\phantom{(}\underline{(x^4+4x^3)\phantom{-bwwww..)}}\\-2x^3-8x-160\phantom{)}\\-~\phantom{}\underline{(-2x^3-8x^2)\phantom{ww...}}\\8x^2-8x-160\phantom{)}\\-~\phantom{}\underline{(8x^2+32x)\phantom{ww...}}\\-40x-160\phantom{)}\\-~\phantom{}\underline{(-40x-160)}\\0\phantom{)}\end{array}`

Therefore, the quotient (answer) of the given division is:

`x^3+\boxed{-2}\:x^2+\boxed{8}\:x+\boxed{-40}`