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Factoring Expressions in Algebra

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Questions and Answers

What is the first step in factoring the expression (3n^7 - 75n^5)?

Divide both sides by \(3n^5\)
Find the greatest common factor of \(3n^7\) and \(75n^5\) (correct)
Factor \(3n^7 - 75n^5\) as a difference of squares
Use the quadratic formula to solve for \(n\)

After factoring out the greatest common factor, what is the remaining expression inside the parentheses?

\((n^4 - 25)\)
\((n^2 - 25)\) (correct)
\((n^2 + 5)\)
\((3n^2 - 25)\)

What is the completely factored form of (3n^7 - 75n^5)?

\((3n^5)(n^2 - 5)(n^2 + 5)\)
\((3n^5)(n^2 + 25)\)
\((3n^5)(n + 5)(n - 5)\) (correct)
\((3n^5)(n^2 - 5)\)

What is the value of the expression (3n^7 - 75n^5) when (n = 2)?

<p>-960 (A)</p> Signup and view all the answers

If we set the expression (3n^7 - 75n^5) equal to zero, how many distinct real solutions for (n) are there?

<p>2 (A)</p> Signup and view all the answers

Flashcards

Factoring

The process of breaking down an expression into its components or factors.

Common factor

A factor that is common to two or more terms, used to simplify expressions.

Difference of squares

A difference of two squares can be factored as (a-b)(a+b).

Polynomial

An algebraic expression consisting of variables and coefficients combined using addition, subtraction, and multiplication.

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Factored form of the expression

The expression written as a product of its factors, showing its complete factorization.

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Study Notes

Factoring the Expression

The expression to factor is 3n⁷ - 75n⁵
The greatest common factor (GCF) of the terms is 3n⁵
Factor out the GCF: 3n⁵(n² - 25)
Recognize that (n² - 25) is a difference of squares
Factor the difference of squares: (n² - 25) = (n - 5)(n + 5)
The completely factored expression is 3n⁵(n - 5)(n + 5)

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