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 in factored form: 7 c 2 − 4 c = c ( 7 c − 4 ) .
The factored form 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 the expression 7 c 2 − 4 c is c ( 7 c − 4 ) .
Examples
Factoring is a useful skill in algebra. For example, if you are trying to find the roots of the quadratic equation 7 c 2 − 4 c = 0 , factoring the expression as c ( 7 c − 4 ) = 0 makes it easy to see that the roots are c = 0 and c = 7 4 . Factoring can also help simplify complex expressions, making them easier to work with.
The expression 7 c 2 − 4 c can be factored by pulling out the common factor c , resulting in the factored form c ( 7 c − 4 ) . This shows both the common factor and the remaining polynomial together. Factoring helps simplify and solve polynomial equations more easily.
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