The previous answer from another person got deleted, so I'm here to put it back in my own words.
(Edit: The answer is A)
First of all, you can take 4 out of each, so simplify everything by 4.
4(x^4 - 6x^3 + 9x^2)
Next, you can see that you're able to take out x^2
4x^2(x^2 - 6x + 9)
You can see that both x^2 and 9 are perfect squares, meaning you can crunch them together like this
(x+3)^2 or (x-3)^2
Of course, only one would work, and as fate has it, (x-3)^ produces x^2 - 6x + 9
This would turn the now factored equation into :
4x^2(x-3)^2 or 4x^2(x-3)(x-3), this means the answer is A
Dividing by a fraction is the same as multiplying by its reciprocal. So dividing by 2/5 will give you the same answer as multiplying by 5/2.
The answer is (-∞.∞).
Draw out a number line. Plot 0 and -4 on the number line.
Shade to the left of x = 0, and have a filled in circle at the endpoint. This is the graph of x≤0
Then graph x ≥−4 by plotting a filled in circle at -4, and shading to the right.
Note how the two graphs overlap to cover the entire real number line
So if we have x≤0 or x≥−4 then we're basically saying x is any real number. To write this in interval notation, we write (−∞,∞)
This is the interval from negative infinity to positive infinity (or just infinity). We exclude each endpoint because we can't actually reach infinity itself. Infinity is not a number. Infinity is a concept
Side note: if you change the "or" to "and", then the solution to x≤0 and x≥−4 would be [-4, 0][−4,0] to indicate the interval from x = -4 to x = 0, including both endpoints. This is the region where the two graphs overlap.
To know more about graphs
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