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:
x
Step-by-step explanation:
Multiples of 12 . . . 12, 24, 36, 48, 60, 72, 84, 96
Multiples of 18 . . . 18, 36, 54, 72, 90
Smallest number that's on both lists . . . 36 .
(12 x 3) = (18 x 2) = 36 .
Answer:
The baseball mitt was $37 and the ball was $7
Step-by-step explanation:
Let m represent the cost of the mitt and let b represent the cost of the ball
Set up a system of equations:
m + b = 44
m = 5b + 2
Solve by substitution by plugging in 5b + 2 as m in the first equation:
5b + 2 + b = 44
Solve for b:
6b + 2 = 44
6b = 42
b = 7
Plug in 7 into the first equation and solve for m:
m + b = 44
m + 7 = 44
m = 37
So, the baseball mitt was $37 and the ball was $7
Answer:
It is six cm。
Step-by-step explanation:
