Question

two students factor 8f^5 - 88f^4. which student is correct? explain.
student a: 8f^4(f - 11)
student b: - 8f^4(-f + 11)
choose the correct answer below.
a. both students are correct. one student factored out a negative 1 while the other did not, but the expressions are equivalent
b. the second student is correct. since subtraction is used in the original expression, negative 1 must be factored out of the expression
c. neither student is correct. the first student incorrectly factored the first term while the second student incorrectly factored the second term
d. the first student is correct. the original expression uses subtraction, so the factored expression must also use subtraction.

Explanation:

Step1: Factor the given expression

We have \(8f^{5}-88f^{4}\). The greatest - common factor of \(8f^{5}\) and \(88f^{4}\) is \(8f^{4}\). Factoring out \(8f^{4}\) from \(8f^{5}-88f^{4}\), we get \(8f^{4}(f - 11)\) (using the distributive property \(ab+ac=a(b + c)\) in reverse, here \(a = 8f^{4}\), \(b=f\) and \(c=- 11\)).

Step2: Analyze Student B's answer

Student B has \(-8f^{4}(-f + 11)\). We can simplify \(-8f^{4}(-f + 11)\) using the distributive property: \(-8f^{4}\times(-f)+(-8f^{4})\times11=8f^{5}-88f^{4}\), which is equivalent to the original expression.

Answer:

A. Both students are correct. One student factored out a negative 1 while the other did not, but the expressions are equivalent