Question

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`?

Answer 1

Degree 5 and 3 terms. See explanation below

Explanation:

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

`p(x)=a_0+a_1x+a_2x^2+a_3x^3+...+a_(n-1)x^(n-1)+a_nx^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(x)=6x^5+3x^2-7x^5-4x^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(x)=(6-7)x^5-4x^3+3x^2=-x^5-4x^3+3x^2` which has three terms