Factoring negative quantity from algebraic expression?

Thread starter Holocene
Start date May 4, 2008
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Expression Factoring Negative

In summary, factoring negative quantity from algebraic expression is a method used to simplify expressions by taking out common factors. It is important because it helps to simplify and solve equations. To factor negative quantity, identify the greatest common factor, divide each term by it, and place the negative sign outside the parentheses. A common mistake is forgetting to place the negative sign outside the parentheses or not identifying the correct greatest common factor.

May 4, 2008

Holocene

Factoring negative quantity from algebraic expression?

Why is this wrong?

[tex]\displaystyle{28xy^2 - 14x = -14x(-2y^2 + 1)}[/tex]

The book instead does this:

[tex]\displaystyle{28xy^2 - 14x = -7x(-4y^2 + 2)}[/tex]

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May 4, 2008

flebbyman

Your book is incorrect

May 4, 2008

Hurkyl

Staff Emeritus

Science Advisor

Gold Member

Those are both valid factorizations.

Related to Factoring negative quantity from algebraic expression?

1. What is factoring negative quantity from algebraic expression?

Factoring negative quantity from algebraic expression is a method used to simplify algebraic expressions by taking out common factors. This means taking out the negative sign from all terms in an expression, and then factoring out the greatest common factor.

2. Why is factoring negative quantity important?

Factoring negative quantity is important because it helps to simplify complicated expressions and make them easier to solve. It also allows us to find the roots of an equation and solve for unknown variables.

3. How do you factor negative quantity from an algebraic expression?

To factor negative quantity from an algebraic expression, first identify the greatest common factor of all the terms in the expression. Then, divide each term by this common factor, and place the negative sign outside the parentheses. Finally, factor out the greatest common factor from the remaining terms inside the parentheses.

4. Can you give an example of factoring negative quantity from an algebraic expression?

Yes, for example, the expression -3x^2 - 6x can be factored as -3x(x + 2). We first identify the greatest common factor, which is -3x. Then, we divide each term by this factor and place the negative sign outside the parentheses. Finally, we factor out the -3x from the remaining terms inside the parentheses.

5. What are some common mistakes to avoid when factoring negative quantity?

Some common mistakes to avoid when factoring negative quantity include forgetting to place the negative sign outside the parentheses, not identifying the greatest common factor correctly, or not factoring out the greatest common factor from the remaining terms inside the parentheses.