Question

rewrite the following polynomial in standard form.\\(x + 9 - 7x^3 - x^4\\)

Explanation:

Step1: Recall standard form of polynomial

The standard form of a polynomial is written in descending order of the exponents of the variable. For a polynomial in one variable \(x\), the standard form is \(a_nx^n + a_{n - 1}x^{n-1}+\cdots+a_1x + a_0\), where \(a_n
eq0\) and \(n\) is a non - negative integer.

Step2: Identify the exponents of each term

• For the term \(x\), the exponent of \(x\) is \(1\) (since \(x = x^1\)).
• For the term \(9\), we can think of it as \(9x^0\) (since \(x^0=1\) for \(x

eq0\)), so the exponent of \(x\) is \(0\).

• For the term \(- 7x^3\), the exponent of \(x\) is \(3\).
• For the term \(-x^4\), the exponent of \(x\) is \(4\).

Step3: Arrange the terms in descending order of exponents

Starting with the term with the highest exponent, which is \(-x^4\) (exponent \(4\)), then the term with exponent \(3\) which is \(-7x^3\), then the term with exponent \(1\) which is \(x\), and finally the term with exponent \(0\) which is \(9\).

So, arranging the terms \(x + 9-7x^3 - x^4\) in standard form, we get \(-x^4-7x^3 + x+9\).

Answer:

\(-x^4 - 7x^3+x + 9\)