What is $24 x^2+14 x$ in factored form?
Answer (2)
Find the greatest common factor (GCF) of the coefficients: GCF(24, 14) = 2.
Identify the common variable factor: x .
Factor out the GCF 2 x from the expression: 24 x 2 + 14 x = 2 x ( 12 x + 7 ) .
The factored form 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 is the largest number that divides both 24 and 14. From the tool, we found that the GCF of 24 and 14 is 2.
Identifying the Common Variable Factor Next, we observe that both terms in the expression, 24 x 2 and 14 x , contain the variable x . The lowest power of x that appears in both terms is x 1 = x . Therefore, x is a common factor.
Factoring out the GCF Now, we factor out the GCF, which is 2 x , from both terms in the expression: 24 x 2 + 14 x = 2 x ( 12 x ) + 2 x ( 7 ) = 2 x ( 12 x + 7 ) So, the factored form of 24 x 2 + 14 x is 2 x ( 12 x + 7 ) .
Examples
Factoring is a fundamental skill in algebra that helps simplify expressions and solve equations. For example, if you're designing a rectangular garden where the area is represented by the expression 24 x 2 + 14 x , factoring it into 2 x ( 12 x + 7 ) can help you determine possible dimensions for the garden. If x represents a unit of length, then 2 x could be the width and ( 12 x + 7 ) could be the length of the garden. This skill is also crucial in more advanced topics like calculus and differential equations.
The factored form of the expression 24 x 2 + 14 x is 2 x ( 12 x + 7 ) . This involves finding the greatest common factor of the coefficients and factoring out the common variable. Factoring helps make complex expressions simpler and more manageable.
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