All categories

2 years ago

When the polynomial in P(x) is divided by (x + a), the remainder equals P(a)

Mathematics

1 answer:

disa [49]2 years ago

7 0

Answer:

This is a false statement:

Step-by-step explanation:

According to Remainder Theorem dividing the polynomial by some linear factor x + a, where a is just some number. As a result of the long polynomial division, you end up with some polynomial answer q(x) (the "q" standing for "the quotient polynomial") and some polynomial remainder r(x).

P(x)= (x+/-a) q(x)+r(x)

P(x)=(x+a) q(x)+r(x). Note that for x=-a

P(-a)=(-a+a) q(-a)+r(-a)= 0* q(-a)+ r(-a)

P(-a)=r(-a)

It means that P(-a) is the remainder not P(a)

Thus the given statement is false....

You might be interested in

The following density function describes a random variable X. f(x) = 1 − (x /2) if 0

Lilit [14]

Answer:

a. Find the probability that X is greater than 1: _P(X>1) = 0.25

b. Find the probability that X is less than .5: _P(X<0.5)_

c. Find the probability that X is equal to 1.5: P(X=1.5)= 0

Step-by-step explanation:

Hello!

The following density function describes a random variable X. f(x) = 1 − (x /2) if 0<x<2 a. Find the probability that X is greater than 1 ________ b. Find the probability that X is less than .5. _________ c. Find the probability that X is equal to 1.5.

First step to calculate the asked probabilities is to integrate the density function.

f(x) = 1 − (x /2) if 0<x<2

$\int\limits^2_0 {(1- (\frac{x}{2}))} \, dx$

$\int\limits^2_0 {1} \, dx - \frac{1}{2} \int\limits^2_0 {x} \, dx$

Now you resolve both integrals:

$\int\limits^2_0 {1} \, dx = x$

$\frac{1}{2} \int\limits^2_0 {x} \, dx = \frac{1}{2} * \frac{x^2}{2} = \frac{x^2}{4}$

$\int\limits^2_0 {(1- (\frac{x}{2}))} \, dx$ = $x-\frac{x^2}{4}$

The cummulative distribution is:

0 for x ≤ 0

$x-\frac{x^2}{4}$ for 0 < x < 2

1 for x ≥ 2

a. Find the probability that X is greater than 1.

P(X>1) = 1 - P(X ≤ 1)

"1" is included in the interval "0 < x < 2", to calculate the probability you have to replace it with $x-\frac{x^2}{4}$ and replace X with 1

1 - P(X ≤ 1) = 1 - ( $1-\frac{1^2}{4}$ )= 1 - 075= 0.25

b. Find the probability that X is less than 0.5.

"0.5" in included in the interval "0 < x < 2", to calculate the probability you have to replace it with $x-\frac{x^2}{4}$ and replace X with 0.5

P(X<0.5)= $0.5-\frac{0.5^2}{4}$ = 0.4375

c. Find the probability that X is equal to 1.5.

"1.5" is included in the interval "0 < x < 2", to calculate the probability you have to replace it with $x-\frac{x^2}{4}$ and replace X with 1.5

This is a continuous variable, in this type of variable the cumulative probability of X=k (k= constant) is always cero.

You can prove it doing the following calculation:

$\int\limits^{1.5}_{1.5} {x-\frac{x^2}{4}} \, dx$ = $1.5-\frac{1.5^2}{4}$ - ( $1.5-\frac{1.5^2}{4}$ ) = 0

I hope it helps!

5 0

2 years ago

A pizza is 10% off the regular price. The discount is $2. How much was the regular price of the pizza? What is the proper set up

tangare [24]

Answer:

The pizza was $20

Step-by-step explanation:

$2/10%= $X/100%

4 0

2 years ago

Please help me with these problems. This is not multiple choice. Part 3

Ivan

9514 1404 393

Answer:

5. 8 ft

6. y = 47x +110; 533 students in 2019

Step-by-step explanation:

4. Answered for you previously. See brainly.com/question/21087377.

Given:

triangular garden with base 7 ft and area 28 ft^2

Find:

height of the triangle

Solution:

The formula for the area of a triangle is ...

A = 1/2bh . . . . . where A is the area, b is the base length, and h is the height

Multiplying by 2/b, we can get a formula for the height. Using this formula, we can solve the problem.

h = 2A/b

We can let h represent the height, and fill in the given data.

h = 2(28 ft^2)/(7 ft)

h = 8 ft

The height of the triangle is 8 feet.

Given:

(0, 110), (5, 345) . . . . . where the points represent ...

(years after 2010, students using the hotline)

Find:

a linear model for the data

the number of students predicted for 2019

Solution:

The 2-point form of the equation for a line is ...

y = (y2 -y1)/(x2 -x1)(x -x1) +y1

where the points are (x1, y1) and (x2, y2). Using the given points, our linear model is ...

y = (345 -110)/(5 -0)(x -0) +110

y = 47x +110 . . . . the linear model, where ...

y is the number of students using the hotline

x is the number of years after 2010

In 2019, x = 9, so y = ...

y = 47(9) +110 = 423 +110 = 533

The number of students predicted to use the hotline in 2019 is 533.

5 0

2 years ago

Read 2 more answers

In his free time, Gary spends 7 hours per week on the Internet and 8 hours per week playing video games. If Gary has five hours

Alborosie

Answer:

Step-by-step explanation:

5x7=35 hours(Gary’s total free time per week)

7+8=15 hours(Gary is spending his time on the internet+Playing video games)

35h.....100%

15.........x%

x=42,8%=>43%

5 0

1 year ago

Enzo is making a scale drawing of the rectangle below.

Nitella [24]

Answer:

Enzo is not correct because he did not multiply the length and width by the same factor.

I do not think Enzo is not correct because he did not multiply the length and width by the same factor.

he is making a drawing of the rectangle below.

A rectangle has a length of 8 centimeters and width of 5 centimeters.

Suppose a new rectangle will have the length of 16 cm.

Enzo says that he can draw an enlarged rectangle that is 16 centimeters by 13 centimeters. Enzo is not correct because he did not multiply the length and width by the same factor.

4 0

2 years ago