Answer: The quotient is (x-2).
Step-by-step explanation:
Since we have given that
![f(x)=(x^3+3x^2-4x-12)\\\\and\\\\g(x)=x^2+5x+6\\\\So,\ \frac{\left(x^3+3x^2-4x-12\right)}{\left(x^2+5x+6\right)}](https://tex.z-dn.net/?f=f%28x%29%3D%28x%5E3%2B3x%5E2-4x-12%29%5C%5C%5C%5Cand%5C%5C%5C%5Cg%28x%29%3Dx%5E2%2B5x%2B6%5C%5C%5C%5CSo%2C%5C%20%5Cfrac%7B%5Cleft%28x%5E3%2B3x%5E2-4x-12%5Cright%29%7D%7B%5Cleft%28x%5E2%2B5x%2B6%5Cright%29%7D)
Now, we have to find the quotient of the above expression.
So, here we go:
![Factorise\ (x^3+3x^2-4x-12)\\\\=\left(x^3+3x^2\right)+\left(-4x-12\right)\\\\=-4\left(x+3\right)+x^2\left(x+3\right)\\\\=\left(x+3\right)\left(x^2-4\right)](https://tex.z-dn.net/?f=Factorise%5C%20%28x%5E3%2B3x%5E2-4x-12%29%5C%5C%5C%5C%3D%5Cleft%28x%5E3%2B3x%5E2%5Cright%29%2B%5Cleft%28-4x-12%5Cright%29%5C%5C%5C%5C%3D-4%5Cleft%28x%2B3%5Cright%29%2Bx%5E2%5Cleft%28x%2B3%5Cright%29%5C%5C%5C%5C%3D%5Cleft%28x%2B3%5Cright%29%5Cleft%28x%5E2-4%5Cright%29)
Now, we will divide the above simplest form with g(x):
![\frac{\left(x+3\right)\left(x^2-4\right)}{\left(x+2\right)\left(x+3\right)}\\\\=\frac{x^2-4}{x+2}\\\\=\frac{\left(x+2\right)\left(x-2\right)}{x+2}\ using\ (a^2-b^2)=(a+b)(a-b)\\\\=x-2](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cleft%28x%2B3%5Cright%29%5Cleft%28x%5E2-4%5Cright%29%7D%7B%5Cleft%28x%2B2%5Cright%29%5Cleft%28x%2B3%5Cright%29%7D%5C%5C%5C%5C%3D%5Cfrac%7Bx%5E2-4%7D%7Bx%2B2%7D%5C%5C%5C%5C%3D%5Cfrac%7B%5Cleft%28x%2B2%5Cright%29%5Cleft%28x-2%5Cright%29%7D%7Bx%2B2%7D%5C%20using%5C%20%28a%5E2-b%5E2%29%3D%28a%2Bb%29%28a-b%29%5C%5C%5C%5C%3Dx-2)
Hence, the quotient is (x-2).
Answer:
-12
Step-by-step explanation:
plug in -1 into the equation which is going to be (4*-1)3
you multiply what is in the parenthesis first and after is going to be (-4)3
lastly your going to multiply -4*3 and it is going to equal to -12.
X will equal -7 in this problem
Answer: 14
Step-by-step explanation:
Input Data :
Point 1 (
x
A
,
y
A
) = (-4, -8)
Point 2 (
x
B
,
y
B
) = (10, -8)
Objective :
Find the distance between two given points on a line?
Formula :
Distance between two points = √
(x
B
−
x
A
)
2
+
(
y
B
−
y
A
)
2
Solution :
Distance between two points = √
(
10
− −
4
)
2
+
(
−
8
− −
8
)
2
= √
14
^2
+
0
^2
= √
196
+
0
= √
196
= 14
Distance between points (-4, -8) and (10, -8) is 14
Answer:
26
Step-by-step explanation:
To evaluate this expression, all we have to do is substitute the given values of the variables into the expression. That is, replace every
in the expression with a
and every
in the expression with a 5.
Doing so, we get:
![p^{2} +m](https://tex.z-dn.net/?f=p%5E%7B2%7D%20%2Bm)
(Substitute given values into the expression)
(Evaluate exponential term)
(Add)
Hope this helps!