Question:
What is the missing expression? [tex]x^8+3x^5=x^5[/tex](______)
Option A: [tex]x+3[/tex]
Option B: [tex]x^2+3[/tex]
Option C: [tex]x^3+3[/tex]
Answer:
Option C:
The missing expression is [tex](x^3+3)[/tex].
Solution:
Given expression is [tex]x^8+3x^5[/tex].
Let us factor the given expression.
There are 2 terms in the expression.
Take out common terms in each of the expression.
[tex]x^8+3x^5=x^5(x^{8-5}+3x^{5-5})[/tex] (use radical rule)
[tex]=x^5(x^3+3x^0)[/tex] (use radical rule)
[tex]=x^5(x^3+3)[/tex]
[tex]x^8+3x^5=x^5(x^3+3)[/tex]
Hence the missing expression is [tex](x^3+3)[/tex].
