Factor the. expression x^2+ 18x +80
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Answer:
Step-by-step explanation:
Step 1: Factor
Answer:
Step-by-step explanation:
x²+18x+80= 0
x²+10x+8x+80=0
x(x+10) +8(x+10)=0
(x+10)(x+8)=0
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Identify the two whole between which the product lies 5×7/10
Tomas learned that the product of the polynomials (a + b)(a2 – ab + b2) was a special pattern that would result in a sum of cubes, a3 + b3. His teacher put four products on the board and asked the class to identify which product would result in a sum of cubes if a = 2x and b = 1.
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Fifth degree polynomial; scary stuff. We know it has five complex roots, counting multiplicities. How many are real?
The rational root test tells us we only have to try the divisors of 9, so 1, -1, 3, -3, 9, -9. We find x=3 gives
243 - 243 - 54 + 54 - 9 + 9 = 0
in nice pairs.
So x-3 is a factor and we can divide to get a 4th degree polynomial. The division is a bit easier than usual.
x^4 - 2x^2 - 3
x - 3 | x^5 - 3x^4 - 2x^3 + 6x^2 - 3x + 9
x^5 - 3x^4
0 - 2x^3 + 6x^2
0 - 3x + 9
0
So we get
It's downhill from here. The new factor is really just a quadratic in x squared, and factors easily:
And now if we descend into irrational and complex numbers, we can further factor
and we can read off our roots,
We have one rational root, namely 3, and two irrational roots, the square roots of three, and two purely imaginary roots.
Answer: 1 rational, 2 irrational
Answer:
One rational and 2 irrational zeroes
Step-by-step explanation:
I agree with the other guy.
f(3) = 0 so x = 3 is a rational root.
There also are 2 irrational roots and 2 complex roots.
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The graph for the function f(x) = 5 - 5x² is shown in the figure below.
How to draw a graph for the function?
- Consider certain values of x to get x-coordinates
- Substitute those values in the function to get y-coordinates
- Coordinate those x and y values as (x, y)
- Plot those points in the graph
- Connect those points, it forms a curve or line or parabola
Calculation:
The given function is f(x) = 5 - 5x²
Consider x = {-1, 0, 1}
When x = -1
f(-1) = 5 - 5(-1)²
= 5 - 5
= 0
∴ (-1, 0)
When x = 0
f(0) = 5 - 5(0)²
= 5 -0
= 5
∴ (0, 5)
When x = 1
f(1) = 5 - 5(1)²
= 5 - 5
= 0
∴ (1, 0)
So, the coordinatepoints are (-1, 0), (0, 5), and (1, 0)
Plotting these points in the graph.
Connecting those points gives a curve shown in the figure below.
Learn more about the graph of a function here:
#SPJ2
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Step-by-step explanation:
To calculate the diameter of a circle, multiply the radius by 2. If you don't have the radius, divide the circumference of the circle by π to get the diameter. If you don't have the radius or the circumference, divide the area of the circle by π and then find that number's square root to get the radius. To find the area of a rectangle multiply its height by its width. For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area.Write down the formula for finding the circumference of a circle using the diameter. The formula is simply this: C = πd. In this equation, "C" represents the circumference of the circle, and "d" represents its diameter. That is to say, you can find the circumference of a circle just by multiplying the diameter by pi.
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Answer:
Step-by-step explanation:
48? i guess. i hope this helps u out with ur question
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