Factor.
$15 x^2+20 x$
Answer (1)
Find the greatest common factor (GCF) of the coefficients 15 and 20, which is 5.
Find the GCF of the variable terms x 2 and x , which is x .
Factor out the GCF 5 x from the expression: 15 x 2 + 20 x = 5 x ( 3 x + 4 ) .
The factored form of the expression 15 x 2 + 20 x is 5 x ( 3 x + 4 ) .
Explanation
Understanding the Problem We are asked to factor the expression 15 x 2 + 20 x . Factoring involves finding the greatest common factor (GCF) of the terms and rewriting the expression as a product of the GCF and the remaining terms.
Finding the GCF of Coefficients First, we identify the coefficients of the terms: 15 and 20. The greatest common factor of 15 and 20 is 5.
Finding the GCF of Variables Next, we look at the variable terms: x 2 and x . The greatest common factor of x 2 and x is x .
Factoring out the GCF Now, we factor out the GCF, which is 5 x , from the expression: 15 x 2 + 20 x = 5 x ( 3 x + 4 ) .
Final Answer Therefore, the factored form of the expression 15 x 2 + 20 x is 5 x ( 3 x + 4 ) .
Examples
Factoring is a fundamental skill in algebra and is used in many real-world applications. For example, suppose you want to find the dimensions of a rectangular garden with an area of 15 x 2 + 20 x square feet. By factoring the expression, you can determine that the dimensions could be 5 x feet by ( 3 x + 4 ) feet. This allows you to plan the layout of your garden efficiently.
