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Chapter 11: Q. 4 (page 764)

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

Short Answer

Expert verified

The given statement is true

Step by step solution

01

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'.

02

Step 2. Find whether the expression is true or false

The polynomial expressions like x2-1 can be factorized further into linear terms but expressions like x2+x+1cannot be factorized further and are non-reducible any further. So we can find both kinds of polynomial functions.

An expression like x2+2x-3cannot be factorized further into linear factors as the coefficients are irrational.

Therefore, the given statement is true.

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Most popular questions from this chapter

In Problems 23–34, graph each system of linear inequalities by hand. Verify your results using a graphing utility

x-2y≤62x-4y≥0

Graph the equation:y=3x+2

Solve each system of equations. If the system has no solution, say that it is inconsistent.
x+3y=52x-3y=-8

Solve each system of equations. If the system has no solution, say that it is inconsistent.
x+2y=-7x+y=-3

In Problems 35–42, graph each system of inequalities by hand.

x2+y2≤9x+y≥3
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