Question

Write the following polynomial in standard form:

$2x^4-\frac{4}{3}x+3x^2+2$

Answer 1

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

$2x^4$ has a degree of $4$

$\frac{4}{3}x$ has a degree of $1$

$3x^2$ has a degree of $2$

$2$ has a degree of $0$

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.

$2x^4+3x^2-\frac{4}{3}x+2$

Hence, the standard form of the polynomial is $2x^4+3x^2-\frac{4}{3}x+2$.