What is $7 c^2-4 c$ in factored form?
Answer (2)
Identify the common factor c in both terms.
Factor out the common factor c from the expression.
Rewrite the expression as a product of the common factor and the remaining terms.
The factored form of the expression 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 the two terms 7 c 2 and − 4 c . Both terms 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 7 c 2 − 4 c is c ( 7 c − 4 ) .
Examples
Factoring is a fundamental skill in algebra that helps simplify expressions and solve equations. For example, if you are designing a rectangular garden with an area represented by the expression 7 c 2 − 4 c , where c is a variable related to the dimensions, factoring the expression into c ( 7 c − 4 ) can help you determine possible dimensions of the garden in terms of c . This technique is also used in physics to simplify equations and in computer science to optimize algorithms.
The expression 7 c 2 − 4 c can be factored to c ( 7 c − 4 ) . By identifying and factoring out the common factor c , we express the original expression in a simpler product form. Thus, the answer is c ( 7 c − 4 ) .
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