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1 answer:
Answer:
Step-by-step explanation:
(A) Since, the velocity can be calculated from the distance time graph, and we can see from the graph that it is constant at every point, thus the graph has the constant velocity.
(B) Average velocity is given by: .
(C) The velocity reflected in the graph is positive in nature.
(D) The point will show that the car is not moving means that the car will cover no more distance in any interval of time, but from the graph we can see that the distance is being covered at equal intervals of time and no such horizontal path is followed, thus, the car is always moving.
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<h3>Answer: Choice B</h3>
f(x) = x^4 - 5x^3 + x^2 + 21x - 18
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Explanation:
The root x = -2 means x+2 is a factor. This is because we add 2 to both sides of x = -2 to get x+2 = 0.
Similarly, x = 3 leads to x-3 being another factor. It's a double root so we really have two copies of (x-3)
The last root is x = 1 which gives the factor x-1.
The four factors are: (x+2)(x-3)(x-3)(x-1)
Let's use the FOIL rule to expand out the first two factors
(x+2)(x-3) = x^2-3x+2x-6 = x^2-x-6
Do the same for the last two factors
(x-3)(x-1) = x^2-1x-3x+3 = x^2-4x+3
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So far we have:
(x+2)(x-3) = x^2-x-6
(x-3)(x-1) = x^2-4x+3
which leads to
(x+2)(x-3)(x-3)(x-1) = (x^2-x-6)(x^2-4x+3)
From here I'll use the box method to multiply these trinomials. Check out the diagram below. Each inner cell is the result of multiplying the headers. Example: x^2 times x^2 = x^4 in the upper left corner.
I've color-coded the inner cells to show the like terms. Add up those like terms:
- -4x^3 + (-x^3) = -5x^3
- 3x^2 + (4x^2) + (-6x^2) = x^2
- -3x + 24x = 21x
Therefore we end up with
(x^2-x-6)(x^2-4x+3) = x^4 - 5x^3 + x^2 + 21x - 18 which is <u>choice B</u>
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To verify this answer, plug in x = 0 and you should get y = -18 to show that we have the correct y intercept. If we tried this with choice A, then we'd get y = 18 which helps eliminate choice A.
Furthermore, plug in x = -2 into choice B and you should get y = 0 as an output. The same applies to x = 3 and x = 1. This confirms that they are roots or x intercepts of the polynomial.
Another way to verify the answer is to use something like WolframAlpha to type in (x+2)(x-3)(x-3)(x-1). Under the "expanded form" subsection, it says x^4 - 5x^3 + x^2 + 21x - 18