What does it mean to factor an algebraic expression?
To factor an algebraic expression means to write it as a product of its factors, which are usually polynomials. This process involves determining the factors that when multiplied together give the original expression. Factoring an expression can help to simplify it, identify common factors, solve equations, and understand the behavior of the function.
Then tell how to factor 35x - 40
To factor the expression 35x - 40, we can first look for a common factor in both terms. In this case, we can divide both terms by 5, giving us:
5(7x - 8)
Now we have factored out the common factor of 5. The expression 7x - 8 cannot be factored further since it is in its simplest form. Therefore, the fully factored expression is:
5(7x - 8)
To factor an algebraic expression means to break it down into its simplest possible form by finding common factors or using other algebraic techniques. The factored form is usually expressed as a product of simpler expressions.
To factor an algebraic expression, follow these steps:
1. Identify any common factors: Look for any common factors that can be factored out of all the terms in the expression. For example, if the expression is 3x + 6, both terms have a common factor of 3. Factoring out this common factor gives you 3(x + 2).
2. Check for special factoring patterns: Certain algebraic expressions have specific factoring patterns that can be used. Some common patterns include perfect square trinomials (Binomial squared) and the difference of squares. By recognizing these patterns, you can simplify the expression further. For example, if you have the expression x^2 - 4, it is a difference of squares and can be factored as (x + 2)(x - 2).
3. Use factoring techniques: If there are no clear common factors or special factoring patterns, you can use factoring techniques such as factoring by grouping or trial and error. Factoring by grouping involves grouping terms together and factoring out common factors within each group. Trial and error involves trying different combinations of factors until a solution is found.
It is important to note that factoring an algebraic expression may not always be possible or may require advanced techniques for more complex expressions. In some cases, the expression may already be completely factored, in which case it cannot be factored any further.