Answer: No, x+3 is not a factor of 2x^2-2x-12
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Explanation:
Let p(x) = 2x^2 - 2x - 12
If we divide p(x) over (x-k), then the remainder is p(k). I'm using the remainder theorem. A special case of the remainder theorem is that if p(k) = 0, then x-k is a factor of p(x).
Compare x+3 = x-(-3) to x-k to find that k = -3.
Plug x = -3 into the function
p(x) = 2x^2 - 2x - 12
p(-3) = 2(-3)^2 - 2(-3) - 12
p(-3) = 12
We don't get 0 as a result so x+3 is not a factor of p(x) = 2x^2 - 2x - 12
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Let's see what happens when we factor p(x)
2x^2 - 2x - 12
2(x^2 - x - 6)
2(x - 3)(x + 2)
The factors here are 2, x-3 and x+2
Hello there!
I'm assuming since there is no question, that you want an explanation for composite functions.
Today, I want to introduce you to a very new way of looking at functions. Think of a function as a machine. I'll call this machine f. When you plug something into this machine, it is an x-value. The machine changes the x-value into a new value which is called a y-value. This is how a function works.
With composite functions though, things get a little bit tricky. To make f(g(x)), you need to plug in x into the g machine, and it will give you an output. (y-value) The next thing you do is take that y-value and plug it into the g machine. The g machine then gives you a new value. This value is f(g(x)).
Let's do an example together...
f(x)=3x and g(x)=x²+4
if we want f(g(x)), first plug in x to the g machine. when plugging in x to the g machine, we get x²+4 as given in the question.
Now we must plug in g(x) into the f machine. Since g(x) is x²+4, we just replace x with x²+4.
We get 3(x²+4)
This means that f(g(x))=3(x²+4)
NOTE: If you are seeking help with an actual question, please message me in the comments and I will assist you shortly!
I hope this helps!
Best wishes :)
Answer:
110 ft
Step-by-step explanation:
The length of fencing is four times the perimeter of one garden.
The formula for the perimeter of a rectangle is
P = 2l + 2w
The total perimeter for all four rectangles is
P = 4× (2l + 2w) = 8l + 8w
Data:
l = 9¼ ft
w = 4½ ft
Calculation:
P = 8l + 8w = 8×9¼ + 8×4½ = 72⁸/₄ + 32⁸/₂ =(72 + 2) + (32 + 4) = 74 + 36 = 110 ft
The total length of fencing is 110 ft.
Answer:
a(a - b)
Step-by-step explanation:
<u>given </u><u>polynomial</u>: a²- ab - 8a + 8a
We can first simplify this answer by removing like terms,
- 8a + 8a = 0
so we have a²- ab in. the simplest form
we can take this one step further and factor out the a (not simplest form)
a time a = a²
a times b = ab
hence, a(a - b)
Learn more about Factoring here: brainly.com/question/18032923
