Question

Write the following polynomials in standard form:

$5x^3+3x^4+x^6-7x^2$

Answer 1

Step 1: Determine the degree of each term in the given expression.

$5x^3$ has a degree of $3$

$3x^4$ has a degree of $4$

$x^6$ has a degree of $6$

$7x^2$ has a degree of $2$

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

Next, write this polynomial in order by degree, highest to lowest.

$x^6+3x^4+5x^3-7x^2$

Hence, the standard form of the polynomial is $x^6+3x^4+5x^3-7x^2$.