Answer:
1. [tex]x^{2} +3[/tex]
2. [tex]x^{2} -5[/tex]
Step-by-step explanation:
1. I'm assuming the equation is [tex](x^{4} + x^{3} +3x^{2} + 3x)[/tex] ÷ [tex](x^{2} +x)[/tex]
-We need to completely factor the original equation
[tex]\frac{x(1+x)(x^{2}+3)}{x(x+1)}[/tex]
-When you divide, you're left with: [tex]x^{2} +3[/tex]
2. Equation: [tex](x^{4} +4x^{3} -5x^{2} -20x)[/tex] ÷ [tex](x^{2} +4x)[/tex]
-Factor completely
[tex]\frac{x(4+x)(x^{2}-5)}{x(x+4)}[/tex]
-Divide; final answer is: [tex]x^{2} -5[/tex]
Just a tip... use symbolab as well to help you with these sort of problems. It'll help you learn how to factor properly step by step, helping understand the objective here.
