Question

Rewrite each polynomial into standard form 1. 6 + x^4 + 2x^5 - 8x2. 3x^3 + x^2 - 11 + 7x3. 9 - 5x 4. -12x + 4x^2 + x^5 5. 4 + 3x^4 - 19x^2 + 3x6. -8 + 9x^2 + 6x

Answer 1

`\begin{gathered} 1.\text{ }2x^5+x^4-8x+6 \\ 2.\text{ }3x^3+x^2+7x-11 \\ 3.\text{ }-5x+9 \\ 4.\text{ }x^5+4x^2-12x \\ 5.\text{ }3x^4-19x^2+3x+4 \\ 6.\text{ }9x^2+6x-8 \end{gathered}`

Explanation:

A polynomial is said to be in its standard form, if it is expressed in such a way that the term with the highest degree is placed first, followed by the term which has the next highest degree, and so on.

Then, for the given polynomials:

1.

`\begin{gathered} 6+x^{4^{}}+2x^5-8x \\ Reorganize\colon \\ 2x^5+x^4-8x+6 \end{gathered}`

2.

`\begin{gathered} 3x^3+x^2-11+7x \\ \text{ Reorganize:} \\ 3x^3+x^2+7x-11 \end{gathered}`

3.

`-5x+9`

4.

`\begin{gathered} -12x+4x^2+x^5 \\ Reorganize\colon \\ x^5+4x^2-12x \end{gathered}`

5.

`\begin{gathered} 4+3x^4-19x^2+3x \\ Reorganize\colon \\ 3x^4-19x^2+3x+4 \end{gathered}`

6.

`\begin{gathered} -8+9x^2+6x \\ Reorganize\colon \\ 9x^2+6x-8 \end{gathered}`