What is $7 c^2-4 c$ in factored form?
Answer (2)
Identify the common factor in the expression.
Factor out the common factor c from both terms.
Write the factored form of the expression as a product.
The factored form of 7 c 2 − 4 c is c ( 7 c − 4 ) .
Explanation
Understanding the Problem We are asked to factor the expression 7 c 2 − 4 c . This means we want to rewrite the expression as a product of simpler expressions.
Identifying Common Factors We look for common factors in both terms of the expression. Both 7 c 2 and − 4 c have a factor of c .
Factoring Out the Common Factor We factor out the common factor c from both terms: 7 c 2 − 4 c = c ( 7 c − 4 ) .
Final Answer The factored form of the expression 7 c 2 − 4 c is c ( 7 c − 4 ) .
Examples
Factoring is a fundamental skill in algebra and is used in many real-world applications. For example, if you want to find the dimensions of a rectangular garden with an area of 7 c 2 − 4 c square feet, where c is a variable representing a certain length, you would factor the expression to find possible expressions for the length and width of the garden. In this case, one possible set of dimensions could be c feet by ( 7 c − 4 ) feet.
The expression 7 c 2 − 4 c can be factored into the form c ( 7 c − 4 ) . This is done by identifying the common factor of c and factoring it out. The final factored expression makes it easier to understand the underlying structure of the original equation.
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