Question

Organize the following polynomial expressions from least to greatest based on their degree: (2 points) I. x + 2xyz II. 3x + y + z III. 2x3y + y2x − 3x + 4 IV. 9x3yz

Answer 1

Answer: II, I, III, IV

Step-by-step explanation:  A polynomial's degree is based off of the term with the highest degree (exponent).  

II. Has the lowest degree because the highest degree in the polynomial is 1, this is because if a variable doesn't have a visible exponent, it's assumed to have an exponent of 1.  

I. Comes second because it's highest degree is 3.  It's three because if you add all of the exponents from the term "2xyz" you get 3.  Think of the term as this, "2x^1y^1z^1" then add them "1+1+1" and you get a degree of 3.

III.  Comes third because it's highest degree is 4, because of the term 2x^3y (2x^3y^1).

IV.  Is last because it has the largest degree of 5, because of the term 9x^3yz (9x^3y^1z^1)

Answer 2

1) x + 2xyz
2) 3x + y + z
3) 2x³y + y²x - 3x + 4
4) 9x³yz

Least to greatest: 2 , 1, 4, 3,

Let us assume that x = 3; y = 2; z = 1 and we disregard the coefficients
1) x + 2xyz  ⇒ 3 + (3)(2)(1) = 9
2) 3x + y + z ⇒ 3 + 2 + 1 = 6
3) 2x³y + y²x - 3x + 4 ⇒ (3³)(2) + (2²)(3) - 3 = 63
4) 9x³yz ⇒ (3³)(2)(1) = 54

Least to greatest ; 2) 6 ; 1) 9 ; 4) 54 ; 3) 63.

We disregarded the coefficients because the expressions are organized based mainly on their degree.