# How do you write a polynomial in standard form, then classify it by degree and number of terms  6x^5+3x^3-7x^5-4x^3?

Mar 15, 2018

Degree 5 and 3 terms. See explanation below

#### Explanation:

A polynomial (n degree) in standard form is given by

$p \left(x\right) = {a}_{0} + {a}_{1} x + {a}_{2} {x}^{2} + {a}_{3} {x}^{3} + \ldots + {a}_{n - 1} {x}^{n - 1} + {a}_{n} {x}^{n}$

where some of ${a}_{i}$ could be zero. If no one of ${a}_{i}$ is zero, the polyinomial is complete, otherwise is incomplete

In our case $p \left(x\right) = 6 {x}^{5} + 3 {x}^{2} - 7 {x}^{5} - 4 {x}^{3}$ is polynomial incomplete of degree 5 (bigest exponent). But we can resume in this equivalent polynomial expression (due to terms of same degree)

$p \left(x\right) = \left(6 - 7\right) {x}^{5} - 4 {x}^{3} + 3 {x}^{2} = - {x}^{5} - 4 {x}^{3} + 3 {x}^{2}$ which has three terms