Question

Write the following polynomials in standard form:

$5x-\sqrt{2}{x}^2+1$

Answer 1

Standard form of a polynomial.

A polynomial written either in the descending powers of $x$ or ascending powers of $x$ is called the standard form of a polynomial in variable $x$. For convenience of calculations we generally write in the descending powers of $x$.

Standard form is $f\left(x\right)=a_n{x}^n+a_{n-1}{x}^{n-1}+a_{n-2}{x}^{n-2}+\dots +a_{1}x+a_0$.

So the standard form of the given polynomial $5x-\sqrt{2}{x}^2+1$ is $-\sqrt{2}{x}^2+5x+1$

Hence, the standard form of the given polynomial is $-\sqrt{2}{x}^2+5x+1$.