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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

The Tortoise and the Hare: In a 21-meter race between a tortoise and a hare, the tortoise leaves 9 minutes before the hare. The hare, by running at an average speed of 0.5 meter per hour faster than the tortoise, crosses the finish line 3minutes before the tortoise. What are the average speeds of the tortoise and the hare?

Solve each system of equations. If the system has no solution, say that it is inconsistent.

x-y=5-3x+3y=2

In Problems 5鈥�24, graph each equation of the system. Then solve the system to find the points of intersection.

y=3x-5;x2+y2=5

Verify that the values of the variables listed are solutions of the system of equations.

x-y=3-3x+y=1x=-2,y=-5;-2,-5

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

2x+y鈮�-22x+y鈮�2
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