Suppose that \(f\) is a polynomial and \(h\) is a polynomial of degree \(5\) or less such that \([(x^2+3x-3)\cdot f(x)+h(x)= -6x^6+72x^4 -50x^3 + 13x^2 +38x -44.\) 

What is the degree of ​\(f\)

Supermathgirl  Apr 5, 2018

The degree of a polynomial is the highest power of x that occurs. The degree of the polynomial on the right hand side is therefore 6. That means the degree of the polynomial on the left hand side must also be 6.  We are told that h(x) is only of degree 5, so the there must be a term in x6 that comes from multiplying f(x) by x2+3x-3.  This means f(x) must have its largest power of x such that when multiplied by x2 it gives x6.  Hence it must have a term with x4 as its largest power of x.  That is, f is of degree 4.

Alan  Apr 6, 2018

9 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.