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 greatest common factor 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 identify the greatest common factor (GCF) of the coefficients, 24 and 14. The GCF of 24 and 14 is 2.
Finding the GCF of the Variables Next, we identify the greatest common factor of the variable terms, 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 given expression.
Final Answer Therefore, the factored form of 24 x 2 + 14 x is 2 x ( 12 x + 7 ) .
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 find that the dimensions could be 2 x feet by ( 12 x + 7 ) feet. This allows you to easily adjust the size of the garden by changing the value of x .
The factored form of the expression 24 x 2 + 14 x is 2 x ( 12 x + 7 ) . To find this, we determined the greatest common factor of the coefficients and the variable terms. By factoring out the GCF, we arrived at the final expression.
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