Mathematics, 18.10.2019 11:30 Eltravieso

Organize the following polynomial expressions from least to greatest based on their degree: i. x + 2xyz ii. 9x3y2 iii. 18x2 + 5ab − 6y iv. 4x4 + 3x2 − x − 4

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1. x + 2xyzdegree of 3 <== this is 2nd
2. 9x^3y^2degree of 5 <== this is 4th
3. 18x^2 + 5ab - 6ydegree of 2 <=== this is 1st
4. 4x^4 + 3x^2 - x - 4degree of 4 <== this is 3rd

** if a polynomial has more then 1 variable, the degree of each term is the sum of the exponentsand the degree of the polynomial is the largest sum.

** if a polynomial has 1 variable, the degree of the polynomial is the highest exponent

Answer from: brazilmade1

The correct order of polynomials in the increasing order of their degree will be 18x^2 + 5ab - 6y , x + 2xyz , 4x^4 + 3x^2 - x - 4 , and 9x^3y^2 . The order will be III>I>IV>II.

The given expressions are:

x + 2xyz, 9x^3y^2, 18x^2 + 5ab - 6y , and 4x^4 + 3x^2 - x - 4 .

The degree of the polynomial x + 2xyz is 3.

The degree of the polynomial 9x^3y^2 is 5.

The degree of the polynomial 18x^2 + 5ab - 6y is 2.

The degree of the polynomial 4x^4 + 3x^2 - x - 4 is 4.

So, the increasing order of the degree will be 2, 3, 4, and 5.

Therefore, the correct order of polynomials in the increasing order of their degree will be 18x^2 + 5ab - 6y , x + 2xyz , 4x^4 + 3x^2 - x - 4 , and 9x^3y^2 . The order will be III>I>IV>II.

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Answer from: Quest

Cbottom left is the correct one.
Question 4) which table does not represent a linear function?

Answer from: Quest

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2:

(2 x^3 + 7 x^2 + (x + 4 x) + 2)/(x (x + 2))

x + 4 x = 5 x:

answer: (2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

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