1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Rashid [163]
2 years ago
6

URGENT!!! 50 POINTS!!! URGENT!!!!!!! Consider the polynomial functions P (x) and Q (x)​ , where neither polynomial is a constant

function.
Determine whether each of the following related functions below will be polynomial function. fill in the blank with Always, Sometimes, or Never for each related function.

P(x) + Q(x)​

P(x) · Q(x)​

P(x) / Q(x)​​

1 / P(x)​​
Mathematics
1 answer:
Nutka1998 [239]2 years ago
7 0

Answer:

Always

Always

Sometimes

Never

Step-by-step explanation:

P(X) + Q(X)

Sum of two polynomials is always a polynomial.

For example, Let P(x) = 3x² and Q(x) = 5x

$ \implies P(x) + Q(x) = 3x² + 5x

This is again a polynomial.

In other words, we can say that Polynomial is closed under addition.

P(x) . Q(x)

Product of two polynomials is again a polynomial.

Let P(x) = 2x and Q(x) = a constant function, 5

Then the product = 10x, is again a polynomial.

Multiplication of two polynomials is closed.

P(x) / Q(x)

This need not always be a polynomial. When Q(x) = a constant function zero, i.e., Q(x) = 0, then the function is not defined.

But let's say P(x) = 5x² and Q(x) = x.

$ \frac{P(x)}{Q(x)} $ = $ \frac{5x^2}{x} $ = 5x, a polynomial.

So, $ \frac{P(x)}{Q(x)} $ is a polynomial sometimes.

We can, say Division is not always closed.

1/Q(x)

This could never be a polynomial. This is not even in the form of a polynomial. So, $ \frac{1}{Q(x)} $ is never a polynomial.

Hence, the answer.

You might be interested in
Is the earth bigger than the sun ​
Ne4ueva [31]

Answer:

The earth is bigger

Step-by-step explanation:

The Earth is bigger than the sun, because 1 million earths can fit inside the sun.

6 0
2 years ago
Read 2 more answers
What Is the wrong way to remember where you caught a lot of fish?
castortr0y [4]
But she would like me and I will get you to do her work on your house so I don’t know if you have any time to do that or if I have a problem I just think she is a better idea if you have her or you have a better job she is so much fun to you and I love her and I will do her love her best and she would be a
5 0
3 years ago
Please help me :):)):):
Verdich [7]

Answer:

12

Step-by-step explanation:

5^2 + b^2 = 13^2

25 + b^2 = 169

169-25= 144

take the square root of 144

answer: 12

3 0
2 years ago
What is the graph of 4x + 7y = -28?
lesya692 [45]

Answer:

StGraph the line using the slope and y-intercept, or two points.

Slope: −47

y-intercept: (0,−4)

x     y

−7    0

0    −4

step-by-step explanation:

5 0
2 years ago
Read 2 more answers
WHO DOESN'T LOVE MAX POINTS. MAX POINT QUESTION<br> PLS ANSWER THIS TRIGONOMETRY QUESTION
mezya [45]

Answer:

Solution given:

opposite:9

adjacent: 12

\theta=?

Relationship between opposite and adjacent is given by tan angle

so

Tan \theta=\frac{opposite} {adjacent}=\frac{9}{12}

Tan \theta=\frac{3}{4}

\theta=Tan^{-1}\frac{3}{4}

\bold{\theta=36.8°}

#11.

hypotenuse[h]=11cm

opposite/perpendicular[P]=b cm

adjacent/base[b]=a cm

now

\theta=62°

Relationship between height and hypotenuse is given by Sin angle

:.

Sin 62°=\frac{opposite}{hypotenuse}=\frac{b}{11}

doing crisscrossed multiplication

b=Sin 62°*11

:.b=9.71 cm

a) At <u>9</u><u>.</u><u>7</u><u>1</u><u> </u>cm height does the ladder touch the building.

again

Relationship between base and hypotenuse is given by Cos angle

:.Cos 62°=\frac{base}{hypotenuse}=\frac{a}{11}

doing crisscrossed multiplication

a=Cos 62°×11

a=5.16cm

b) the distance between the foot of the ladder and the building is <u>5.16cm.</u>

4 0
2 years ago
Other questions:
  • 2- (-8) + (-3)=<br> 7<br> 12<br> 1<br> 14
    7·2 answers
  • Which of the following statements are true about the equation below?
    6·2 answers
  • Sam and Annika ride their bike to school. Sam rides his bike (k) kilometers. Annika rides her bike 2 less than 4 times as many k
    14·1 answer
  • Consider the inequality-5(x+7)&lt;-10 write an inequality representing the solution for x
    11·1 answer
  • Which triangle can be proven congruent to triangle ABC?
    14·2 answers
  • Simplify (2y-1)(4y-3)
    9·1 answer
  • What is the solution for the following system of equations?<br> 2x + y = 7<br> x - 2y = 6
    8·1 answer
  • A statistician calculates the mean from several random surveys, each of adults in Virginia, to find out the most frequent type o
    6·2 answers
  • Pls help me with the rest of this. I need it today.
    8·1 answer
  • Subtract: (–3x2 + 7 – 2x) – (6 + 7x – 4x2)
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!