Factor completely x3 + 8x2 − 3x − 24. (x − 8)(x2 − 3) (x + 8)(x2 + 3) (x − 8)(x2 + 3) (x + 8)(x2 − 3)
1 answer:
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Answer:
Step-by-step explanation:
a = 3
b = 3
c = 1
Discriminate = sqrt(b^2 - 4ac)
Discriminate = sqrt(9 - 4*3*1)
Discriminate = sqrt(9 - 12)
Discriminate = sqrt(-3)
What negative value means that there are no real roots and the y intercept = 1. You should always graph this kind of question, which I am doing for you. I use Desmos which is a very handy program.
You should notice that the minimum is above the x axis. That means there are no real roots, just as the discriminate tells you.
Both functions decrease at (-1, 2)
<h3>How to determine the decreasing intervals of the function?</h3>The complete question is added as an attachment
The polynomial function f(x) is represented by the graph.
From the graph, the polynomial function decreases at (-2, 2)
The absolute function is given as;
f(x) = =5|x + 1| + 10
The vertex of the above function is
Vertex = (-1, 10)
Because a is negative (a= -5), the vertex is a maximum.
This means that the function decreases at (-1, ∞)
So, we have
(-2, 2) and (-1, ∞)
Combine both intervals
(-1, 2)
This means that both functions decrease at (-1, 2)
See attachment 2 for the number line that represents the interval where both functions are decreasing
Read more about function intervals at:
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