What is $24 x^2+14 x$ in factored form?
Answer (2)
Find the greatest common factor (GCF) of the coefficients 24 and 14, which is 2.
Find the GCF of the variables x 2 and x , which is x .
Factor out the GCF 2 x from the expression 24 x 2 + 14 x .
The factored form of the expression is 2 x ( 12 x + 7 ) .
Explanation
Understanding the Problem We are asked to factor the expression 24 x 2 + 14 x . This means we want to rewrite the expression as a product of simpler expressions.
Finding the GCF of the Coefficients First, we need to find the greatest common factor (GCF) of the coefficients, which are 24 and 14. The GCF of 24 and 14 is 2.
Finding the GCF of the Variables Next, we find the GCF of the variable terms, which are x 2 and x . The GCF of x 2 and x is x .
Factoring out the GCF Now, we factor out the GCF, which is 2 x , from the expression 24 x 2 + 14 x . We divide each term by 2 x :
2 x 24 x 2 = 12 x 2 x 14 x = 7
Writing the Factored Form So, we can rewrite the expression as: 24 x 2 + 14 x = 2 x ( 12 x + 7 ) This is the factored form of the expression.
Examples
Factoring is a fundamental skill in algebra and is used in many real-world applications. For example, if you are designing a rectangular garden with an area of 24 x 2 + 14 x square feet, you might want to find the dimensions of the garden in terms of x . By factoring the expression, you can determine that the garden could have a width of 2 x feet and a length of ( 12 x + 7 ) feet. This helps in planning the layout and managing resources effectively.
To factor the expression 24 x 2 + 14 x , we find the greatest common factor (GCF), which is 2 x . Factoring this out gives us the result 2 x ( 12 x + 7 ) . This helps simplify the expression and is a valuable skill in algebra.
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