Question

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

Short answer

The given statement is true

Step-by-step solution

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.