The remainder when f(x) is divided by (x - 3)(x - 1)^2 is (6x - 3).
<h3>What is the remainder theorem for polynomials?</h3>
If there is a polynomial p(x), and a constant number 'a', then
where g(x) is a factor of p(x)
Here, f(x) is the given polynomial.
By Remainder Theorem,
When divided by (x-3),
f(3) = 15........(1)
When divided by (x-1)²,
f(1) = 2x - 1........(2)
Another polynomial is (x - 3)(x - 1)²
= (x - 3)(x - 1)(x -1)
So,
f(x) = (x - 3)(x - 1)(x -1)Qx + (ax+b)
For f(1),
2x + 1 = a + b
3 = a + b
For f(3),
15 = 3a + b
or, 15 = 3a + 3 - a
or, 15 = 3 + 2a
or a = 6
Also, b = -3
Hence, the remainder is (6x - 3).
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Answer:
1. x=25
2.x=17/2
3.x=20
4.x=6
Step-by-step explanation:
1.x-23=2
x=2+23
x=25
2.
x+1/2=9
x=9-1/2
(have to make the denominators same)
x= 18/2 - 1/2
x=17/2
3.
x/10=2
x=2 × 10
x=20
4.
2x=12
x=12/2
x=6
Use Pythagoras theorem
13^2 = 12^2 + x^2
x^2 = 13^2 - 12^2
x^2 = 169 - 144 = 25
x = 5 ft answer
Velocity (against wind) = 2,688 km / 4 hr = 672 km/hr
Velocity (with wind) = 3,208 km / 4 hr = 802 km/hr
psa means plane velocity in still air
ws means wind speed
psa -ws = 672
psa +ws = 802 We add both equations and get
2 psa = 1,474
plane velocity (in still air) = 737 km/hr
psa +ws = 802 so that means
wind speed = 802 -737 = 65 km/hr
Source:
http://www.1728.org/veloccal.htm
(My website)