Which algebraic expression is a polynomial with a degree of 5?

3x5 + 8x4y2 – 9x3y3 – 6y5
2xy4 + 4x2y3 – 6x3y2 – 7x4
8y6 + y5 – 5xy3 + 7x2y2 – x3y – 6x4
–6xy5 + 5x2y3 – x3y2 + 2x2y3 – 3xy5

The correct answer is:  [B]:

            →    " 2xy⁴  + 4x²y³ – 6x³y² – 7x⁴ " .

Note:

This answer choice is a polynomial with a degree of "5" .

Note that there are 2 (TWO) variables in this polynomial expression
  (in this very "correct answer choice:  [B]:  
      →  which are:  "x" and "y" .

Consider each "term" in the polynomial given in

{ this correct answer choice:  [B] } :

      →  " 2xy⁴  + 4x²y³ – 6x³y² – 7x⁴ " ; 

1)  " 2xy⁴ " ;  the degree is "5" ;  
       →  since " 2xy⁴ = 2x¹y⁴ " ;  
       →  and from " x¹y⁴ " ; the degree is:  " 4 + 1 = 5 " .

2)  " 4x²y³ " ;  the degree is "5" ;  
       →  since from: " x²y³ " ; the degree is:  " 2 + 3 = 5 " .
 
3)  " 6x³y² " ; the degree is: "5" ; 
      →  since from: " x³y² " ; the degree is:  " 3 + 2 = 5 " .

4)  " 7x⁴ " ;  the degree is "4" ; 
      →  since "4" is the only exponent of the only variable in the expression.

Since "5" is the highest degree of all of the terms in the polynomial; 
      → the degree of the polynomial is:  "5" .


Consider the other answer choices:

 Choice:  [A]:  " 3x⁵ + 8x⁴y² – 9x³y³ – 6y⁵ " ;  is incorrect.

     →  By looking at the entire expression, we can see that the highest degree is at least "5" {that is; from the terms:  " 3x⁵ "  and  "6y⁵ " .  However, the other terms show us that the highest degree is "6" ;  which is greater than "5". 

    →  Note:  " 8x⁴y² " ;  4 + 2 = 6;  
                    " 9x³y³ " ;  3 + 3 = 6 ;

 Choice:  [C]:  " 8y⁶ + y⁵ – 5xy³ + 7x²y² – x³y – 6x⁴ " ; is incorrect.
 
    → Note:  From the first term in the expression:  

                 " 8y⁶ " ;  → we can already tell that the degree of the expression is [at least] "6" ; which is greater than "5" .                                                                  

     {Note:  "6" is the only variable assigned to the only exponent within this term of the expression.}.

 Choice:  [D]:  " –6xy⁵ + 5x²y³ – x³y² + 2x²y³ – 3xy⁵ " ;  is incorrect.
 
    → Note:  From the first term in the expression:  
               " –6xy⁵ " ;  → we can already tell that the degree of the expression is [at least] "6" ; which is greater than "5" . 

    → Note:  " –6xy⁵ " =  " –6x¹y⁵ " ;
 
              → from: " x¹y⁵ " ;  →  " 1 + 5 = "6" .