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ElenaW [278]
3 years ago
13

How can I tell, when doing synthetic division, if the binomial is a FACTOR of the dividend?

Mathematics
1 answer:
Alecsey [184]3 years ago
5 0

If you get 0 as the last value in the bottom row, then the binomial is a factor of the dividend.

Let's say the binomial is of the form (x-k) and it multiplies with some other polynomial q(x) to get p(x), so,

p(x) = (x-k)*q(x)

If you plug in x = k, then,

p(k) = (k-k)*q(k)

p(k) = 0

The input x = k leads to the output y = 0. Therefore, if (x-k) is a factor of p(x), then x = k is a root of p(x).

It turns out that the last value in the bottom row of a synthetic division table is the remainder after long division. By the remainder theorem, p(k) = r where r is the remainder after dividing p(x) by (x-k). If r = 0, then (x-k) is a factor, p(k) = 0, and x = k is a root.

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Jada purchases a sweater for $36. The store charges her 8% sales tax on the purchase. How much sales tax will the store charge o
dusya [7]

Answer:

Step-by-step explanation:

36/100=0.36 - 1%

8*0.36=2.88$

6 0
2 years ago
Triangle ABC is an isosceles with a base AC. The base angles are 60 degrees. Find the length of the base and the length of the a
lisabon 2012 [21]

Answer:

base =5   because all angles=60, so an equilateral triangle

height=4.33

Step-by-step explanation:

height^2+1/2(5)^2=5^2

height^2+6.25=25

height^2=18.75

height=4.33

8 0
2 years ago
The rule below shows how to find the position of an object thrown upward with initial velocity of 15 feet per second. Which answ
nekit [7.7K]

Here we're applying a basic physics rule for vertical motion where the only pull on the object is gravity.


This rule has the form


h(t) = h + v t + (1/2)a*t^2

o o


To adapt this rule to this particular question replace h with 0, as the

o

upward path of the object begins at 0 ft. Replace v with +15 ft/sec.

o


Replace "a" with (-32.2 ft/(sec^2); this is the acceleration due to gravity.


Then we have the following, with the label F(t):


F(t) = 0 + (15 ft/sec)t + (1/2)(-32.2 ft)/(sec^2), or


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Please note: To avoid confusion, please use " ^ " to denote exponentiation:


F(t) = -16t^2 + 15t

5 0
3 years ago
Read 2 more answers
10)
Kipish [7]

Answer:

-600

Step-by-step explanation:

The rate of change of a function f(x) in a certain interval (x_1,x_2) is the ratio between the change of the function and the change in the value of x:

r=\frac{f(x_2)-f(x_1)}{x_2-x_1}

The rate of change of a function tells how much the value of the function is changing per change in unit of x: therefore, for a linear function it corresponds to the slope of the line.

In this problem, the function f(x) is equal to the value of the business machine in dollars, while the variable x represents the number of years.

Here we are told that the machine was purchased for

q=\$4500

while its value decreases by $600 each year, so

m=-600\$

This means that the linear function that represents the value of the machine after x years is:

y=4500-600x

Therefore, the rate of change of the function is -600.

3 0
3 years ago
4. An object is at rest if all forces
algol13

Answer:

+5.5

Step-by-step explanation:

Lets say you have an apple and you apply -5.5 newtons of force to it, for it to be balanceds you have to push the opposite, which is +5.5 newtons.

3 0
2 years ago
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