The remainder theorem says that dividing a polynomial <em>f(x)</em> by a 1st-degree polynomial <em>g(x)</em> = <em>x</em> - <em>c</em> leaves a remainder of exactly <em>f(c)</em>.
(a) With <em>f(x)</em> = <em>px</em> ³ + 4<em>x</em> - 10 and <em>d(x)</em> = <em>x</em> + 3, we have a remainder of 5, so
<em>f</em> (-3) = <em>p</em> (-3)³ + 4(-3) - 10 = 5
Solve for <em>p</em> :
-27<em>p</em> - 12 - 10 = 5
-27<em>p</em> = 27
<em>p</em> = -1
(b) With <em>f(x)</em> = <em>x</em> + 3<em>x</em> ² - <em>px</em> + 4 and <em>d(x)</em> = <em>x</em> - 2, we have remainder 8, so
<em>f</em> (2) = 2 + 3(2)² - 2<em>p</em> + 4 = 8
-2<em>p</em> = -10
<em>p</em> = 5
(you should make sure that <em>f(x)</em> was written correctly, it's a bit odd that there are two <em>x</em> terms)
(c) <em>f(x)</em> = 2<em>x</em> ³ - 4<em>x</em> ² + 6<em>x</em> - <em>p</em>, <em>d(x)</em> = <em>x</em> - 2, <em>R</em> = <em>f</em> (2) = 18
<em>f</em> (2) = 2(2)³ - 4(2)² + 6(2) - <em>p</em> = 18
12 - <em>p</em> = 18
<em>p</em> = -6
The others are done in the same fashion. You would find
(d) <em>p</em> = 14
(e) <em>p</em> = -4359
(f) <em>p</em> = 10
(g) <em>p</em> = -13/2 … … assuming you meant <em>f(x)</em> = <em>x</em> ⁴ + <em>x</em> ³ + <em>px</em> ² + <em>x</em> + 20
Answer:
Step-by-step explanation:
Let’s break this apart.
Box= 12cm x 8cm x 6cm
Cube= 2cm x 2cm x 2cm
How many cubes fit in the box?
calculate the volume of the box. To do this, multiply the length by the width by the height (L x W x H)
12 x 8 x 6 = 576cm cubed
2. Calculate the volume of the cube. Once again we multiply L x W x H
2 x 2 x 2 = 8cm cubed
3. Next we divide the volume of the box by the volume of the cube
576 / 8 = 72 cubes
Therefore, it would take 72 cubes to fill a box.
Answer:
11.75 = 5.25 + x
x = 6.50
Step-by-step explanation:
Answer: 6,000
If the value before the one you are rounding to is 5 or greater then round up. If it is 4 or less round down.
I am not seeing a picture so I am going to give you the instructions to do it yourself. All you would have to do is divide the total perimeter (35 centimeters) by however many sides the polygon has. For example, if it was a pentagon, then the equation would be 35/5, which would equal 7.
