Chapter 11: Q1. (page 727)

State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence.
The least common multiply for $x^{2} - 25$ and $x - 5$ isrole="math" localid="1648029600853" $\underline{x - 5}$ .

Short Answer

Expert verified

The given statement is false.

The corrected statement is “The least common multiply for $x^{2} - 25$ and $x - 5$ is $\underline{x^{2} - 25}$ .”.

Step by step solution

Step 1. State the concept of least common multiple.

The least common multiple (LCM) is the least number that is a multiple of two or more numbers or polynomials.

Step 2. Explanation of the statement.

The expression is as follows $x^{2} - 25$ and $x - 5$ .

Calculate the prime factors of both the expressions:

role="math" localid="1648029852221" $x^{2} - 25 = (x + 5) \cdot (x - 5) x - 5 = 1. (x - 5)$

Use each prime factor $(x + 5)$ and $(x - 5)$ , the greatest number of times it appears in either of the factorizations.

role="math" localid="1648029943926" $LCM = (x + 5) \cdot (x - 5) = x^{2} - 25$

Step 3. Write whether the statement is true or false.

The given statement “The least common multiply for $x^{2} - 25$ and $x - 5$ is .localid="1648030000920" $\underline{x - 5}$ ” is false and the corrected statement will be “The least common multiply for $x^{2} - 25$ and $x - 5$ is $\underline{x^{2} - 25}$ .”.

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State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence.
The least common multiply for $x^{2} - 25$ and $x - 5$ isrole="math" localid="1648029600853" $\underline{x - 5}$ .

Short Answer

Step by step solution

Step 1. State the concept of least common multiple.

Step 2. Explanation of the statement.

Step 3. Write whether the statement is true or false.

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State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence.The least common multiply forx2−25 andx−5 isrole="math" localid="1648029600853" x−5¯.

Short Answer

Step by step solution

Step 1. State the concept of least common multiple.

Step 2. Explanation of the statement.

Step 3. Write whether the statement is true or false.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Logic and Functions

Discrete Mathematics

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence.
The least common multiply for $x^{2} - 25$ and $x - 5$ isrole="math" localid="1648029600853" $\underline{x - 5}$ .