Question

a student is asked to factor r^{10}+r^{8} completely. is the students work correct? explain. r^{10}+r^{8} 10 8 ②5 ②4 r^{2}(r^{5}+r^{4}) choose the correct answer below a. the students work is incorrect. since r^{10} is r multiplied together 10 times and r^{8} is r multiplied together 8 times, the common factor is r^{8} b. the students work is incorrect. the student did not find the correct factors of the exponents but still removed the common factor. c. the students work is incorrect. the student found the correct factors of the exponents but did not remove the common factor. d. the students work is correct. the student found the correct factors of the exponents and removed the common factor.

Explanation:

Step1: Recall factoring rule for terms with exponents

When factoring $r^{m}+r^{n}$ ($m>n$), the greatest - common factor is $r^{n}$. Here, for $r^{10}+r^{8}$, the GCF of $r^{10}$ and $r^{8}$ is $r^{8}$ since $r^{10}=r^{8}\times r^{2}$ and $r^{8}=r^{8}\times1$.

Step2: Analyze student's work

The student factored out $r^{2}$ and got $r^{2}(r^{5}+r^{4})$. This is incorrect because the student did not factor out the greatest - common factor. The correct factoring is $r^{8}(r^{2} + 1)$.

Answer:

A. The student's work is incorrect. Since $r^{10}$ is $r$ multiplied together 10 times and $r^{8}$ is $r$ multiplied together 8 times, the common factor is $r^{8}$