Write the following polynomial in standard form:
$2 x^{3} + 5 x - x^{2} - x^{5}$

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Solution

Step 1: Determine the degree of each term in the given expression.
$2 x^{3}$ has a degree of $3$
$5 x$ has a degree of $1$
$x^{2}$ has a degree of $2$
$x^{5}$ has a degree of $5$
Step 2: Write the standard form of a polynomial.
A polynomial is said to be in standard form if the exponents of a variable involved decrease or increase as we move from left to right.
It is represented by $f (x) = a_{n} x^{n} + a_{n - 1} x^{n - 1} + a_{n - 2} x^{n - 2} + \dots + a_{1} x + a_{0}$ .
Next, write this polynomial in order by degree, highest to lowest.
$- x^{5} + 2 x^{3} - x^{2} + 5 x$
Hence, the standard form of the polynomial is $- x^{5} + 2 x^{3} - x^{2} + 5 x$ .

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