Question

Factor the following expression completely: x^(3)+10x^(2)+1x+10

Answer 1

To factor the expression x^3+10x^2+x+10 completely, we can use the grouping method followed by factoring by grouping. The factored form of the expression is (x+10)(x^2+1).

Step-by-step explanation:

To factor the expression x^3+10x^2+x+10 completely, we can use the grouping method followed by factoring by grouping.

1. 
   
2. Group the terms into two pairs:
3. 
   

• 
  
• x^3+10x^2
• 
  
• x+10
• 
  

Factor out the greatest common factor from each pair:

• 
  
• x^2(x+10)
• 
  
• 1(x+10)
• 
  

Notice that both pairs have a common factor of (x+10). Factor out this common factor:

• 
  
• x^2(x+10)+1(x+10)
• 
  

This gives us the factored form: (x+10)(x^2+1)

Learn more about Factoring Polynomials