If P(x) is the product of a linear polynomial and a cubic polynomial, how many roots does P(x) = 0 have?Explain

Mathrules May 19, 2019

#1**0 **

The degree of the polynomial determins how many roots it has.

If you have the linear polynomial \(ax+b\) and the cubic polynomial \(cx^3+dx^2+ex+f\), the highest power in the product \((cx^3+dx^2+ex+f)(ax+b)=acx^4+(ad+bc)x^3+(ae+bd)x^2+(af+be)x+bf\) is \(x^4\) so the polynomial will have 4 roots.

power27 May 19, 2019