Question

wo students factor 8 f Superscript 5 Baseline minus 80 f Superscript 4. Which student is​ correct? Explain.
Student A
Student B
8 f Superscript 4 Baseline left parenthesis f minus 10 right parenthesis
negative 8 f Superscript 4 Baseline left parenthesis negative f plus 10 right parenthesis
Question content area bottom
Part 1
Choose the correct answer below.
A.
Neither student is correct. The first student incorrectly factored the first term while the second student incorrectly factored the second term.
B.
The second student is correct. Since subtraction is used in the original​ expression, negative 1 must be factored out of the expression.
C.
The first student is correct. The original expression uses​ subtraction, so the factored expression must also use subtraction.
D.
Both students are correct. One student factored out a negative 1 while the other did​ not, but the expressions are equivalent.

Answer 1

D. Both students are correct.

Explanation: 8f^4(f − 10) expands to 8f^5 − 80f^4, and
−8f^4(−f + 10) = (−8f^4)(−1)(f − 10) = 8f^4(f − 10),
so both factorizations are equivalent (Student B has factored out an extra −1).