15 inches measurement yes or no

ch4aika [34]

-3   | 1   0   0   0   0   243 $\longleftarrow$ coefficients of the polynomial you're dividing
.     |                                   $\longleftarrow$ drop down the leading coefficient
- - - - - - - - - - - - - - - - - - -
.     | 1

On the left side of the frame, we write -3 because we're dividing by $x+3=x-(-3)$ . (The algorithm is followed for division of a polynomial by a factor of $x-c$ .) Since we're dividing a degree 5 polynomial by a degree 1 polynomial, we expect to get a degree 4 polynomial.

-3   | 1   0   0   0   0   243
.     |      -3                         $\longleftarrow$ multiply -3 by 1, write in next column, add to 0
- - - - - - - - - - - - - - - - - - -
.     | 1 -3

Repeat step for the remaining columns.

-3   | 1   0   0   0   0   243
.     |      -3   9
- - - - - - - - - - - - - - - - - - -
.     | 1 -3   9

-3   | 1   0   0      0   0   243
.     |      -3   9   -27
- - - - - - - - - - - - - - - - - - -
.     | 1 -3   9   -27

-3   | 1   0   0      0 0   243
.     |      -3   9   -27   81
- - - - - - - - - - - - - - - - - - - - -
.     | 1 -3   9   -27   81

-3   | 1   0   0      0 0 243
.     |      -3   9   -27   81 -243
- - - - - - - - - - - - - - - - - - - - -
.     | 1 -3   9   -27   81       0

which translates to

$\dfrac{x^5+243}{x+3}=x^4-3x^3+9x^2-27x+81$

So the bottom row of the frame gives the coefficients of each term in the quotient by descending order. Since the last coefficient is 0, this means the remainder upon division vanishes, i.e. $x^5+243$ is exactly divisible by $x+3$ .

- - -

Another way to get the same result is to use a well-known result: for $a+b\neq0$ ,

$a^5+b^5=(a+b)(a^4-a^3b+a^2b^2-ab^3+b^4)\implies\dfrac{a^5+b^5}{a+b}=a^4-a^3b+a^2b^2-ab^3+b^4$

and in this case $a=x$ and $b=3$

3 0

4 years ago

Gift shop buys cards at $3.50 each. mark them up 80%. What do they sell them for?

pantera1 [17]

Oh what's 80 percent of 3.50 well think of 100 percent is 3.50 and then keep on subtracting until you have 80 percent of what you have

3 0

3 years ago

Read 2 more answers

What is the sum for quadrilateral

mihalych1998 [28]

Answer:

360 degrees

Step-by-step explanation:

The sum of all interior angles in a quadrilateral is 360 degrees.

8 0

3 years ago

Find the mean of the data in the pictograph below.

Irina-Kira [14]

<u>Final Answer:</u>

mean = 4 sundaes

<u>Solution:</u>

each bowl of sundaes contains 3 sundaes.

two scoops = 4 sundae bowls
I scream = 6 sundae bowls
dream scream = 2 sundae bowls

Sundays = 4 sundae bowls

(plus 3, the number three represents how many sundae's there are in a bowl)

(divide it by 12, since there are 12 numbers in the data set)

Mean = (4 + 4 + 4 + 6 + 6 + 6 + 2 + 2 + 2 + 4 + 4 + 4) ÷ 12

= 48 ÷ 12 = 4

8 0

3 years ago

Jeremy uses 2 feet 3 inches of board for each birdhouse he builds. How many inches of board does he need to make 6 birdhouses? U

Pavel [41]

Answer:

The length of board required is 13 feet 6 inches .

Step-by-step explanation:

Board required to make one bird house = 2 feet 3 inches

= 2 x 12 + 3 = 27 inches

Number of bird houses = 6

So, the board required

= 6 x 27 = 162 inches

13.5 feet = 13 feet 6 inches

4 0

3 years ago