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#?

↳Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
1 Answer
F. Javier B.
Mar 15, 2018

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

Related questions
See all questions in Polynomials in Standard Form
Impact of this question
2229 views around the world
You can reuse this answer
Creative Commons License