Q. 4 - Precalculus Enhanced with Graphing Utilities

Question

True or False Every polynomial with real numbers as coefficients can be factored into products of linear and/or irreducible quadratic factors. 

Step-by-Step Solution

Answer

The given statement is true

Step 1. Given statement

The given statement is 'Every polynomial with real numbers as coefficients can be factored into products of linear and/or reducible quadratic factors'.

Step 2. Find whether the expression is true or false

The polynomial expressions like $x^2-1$  can be factorized further into linear terms but expressions like $x^2+x+1$ cannot be factorized further and are non-reducible any further. So we can find both kinds of polynomial functions.

An expression like $x^2+\sqrt{2}x-\sqrt{3}$ cannot be factorized further into linear factors as the coefficients are irrational.

Therefore, the given statement is true.