Question

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

Answer 1

The Degree is the largest exponent of that variable.

Let's get started :

$3x^5 + 8x^4y^2 - 9x^3 y^3 - 6y^5$

Here, the largest exponent is from $8x^4y^2$. It's 4+2 = 6.

$8y^6 + y^5 - 5xy^3 + 7x^2y^2 - x^3y - 6x^4$

Here, the largest exponent is 6.

$-6xy^5 + 5x^2y^3 - x^3y^2 + 2x^2y^3 - 3xy^5$

Here, the largest exponent is also 6. x itself is considered as exponent 1. So 1+5 = 6.

At last, let's check the second option, 

$2xy^4 + 4x^2y^3 - 6x^3y^2 - 7x^4$

Here the largest exponent is 5.

In short, the answer would be :

$\boxed {\boxed{2xy^4 + 4x^2y^3 - 6x^3y^2 - 7x^4}}$

Hope this helps !

Photon

Answer 2

The correct answer is:  [B]:
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            →    " 2xy⁴  + 4x²y³ – 6x³y² – 7x⁴ " .
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Note:
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This answer choice is a polynomial with a degree of "5" .
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Note that there are 2 (TWO) variables in this polynomial expression
  (in this very "correct answer choice:  [B]:  
      →  which are:  "x" and "y" .
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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" .
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Consider the other answer choices:
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 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 ;
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 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.}.
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 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" .
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