Answer:
![a) f(x)=3x^{3}-6x^{2}-15x+30](https://tex.z-dn.net/?f=a%29%20f%28x%29%3D3x%5E%7B3%7D-6x%5E%7B2%7D-15x%2B30)
Step-by-step explanation:
1) In this question we've been given "a", the leading coefficient. and two roots:
![x_{1}=\sqrt{5}\:x_{2}=2](https://tex.z-dn.net/?f=x_%7B1%7D%3D%5Csqrt%7B5%7D%5C%3Ax_%7B2%7D%3D2)
2) There's a theorem, called the Irrational Theorem Root that states:
If one root is in this form
then its conjugate
. is also a root of this polynomial.
Therefore
![x_3=-\sqrt{5}](https://tex.z-dn.net/?f=x_3%3D-%5Csqrt%7B5%7D)
3) So, applying this Theorem we can rewrite the equation, by factoring. Remembering that x is the root. Since the question wants it in this expanded form then:
![f(x)=3(x-\sqrt{5})(x+\sqrt{5})(x-2)\Rightarrow 3x^{3}-6x^{2}-15x+30](https://tex.z-dn.net/?f=f%28x%29%3D3%28x-%5Csqrt%7B5%7D%29%28x%2B%5Csqrt%7B5%7D%29%28x-2%29%5CRightarrow%203x%5E%7B3%7D-6x%5E%7B2%7D-15x%2B30)
-6x^2+4x
my reasoning:
eliminate the opposites (5 & -5)
collect the like terms (-8x^2 & + 2x^2)
collect the like terms again (-3x &+7x)
Answer:
The student took 2.5 minutes to paint 1 square foot.
Step-by-step explanation:
In order to know how long the student took to paint each square foot we first need to know the total area of the bulletin board. Since it is a rectangle we can compute it's area by multiplying the width and the height. That is:
area = 2*3 = 6 square foot
Since the student took 15 minutes to paint the whole board the pace at which he was working can be calculated by dividing the total area of the board by the time he took to paint all of it. So we have:
pace = 6/15 = 0.4 foot/min
To find how long it took him to paint 1 square foot we can divide it by the pace he was painting. We have:
time = 1/0.4 = 2.5 minutes
The student took 2.5 minutes to paint 1 square foot.
Answer:
The answer is c
Step-by-step explanation: