You can do synthetic division twice immediately (or once if you know how to handle x^2 - 25 all at once. I'll use 2 divisions. x^2 - 25 is (x + 5)(x - 5). Both of them are zeros to the given equation which means that x = +5 and
x = - 5 are both zeros of the given quartic.
5 1 -2 -33 50 200
5 15 -90 -200
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1 3 -18 -40 0
What you have now is x^3 + 3x^2 - 18x - 40 = 0
Do another synthetic division
-5 1 3 -18 -40
-5 10 40
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1 -2 -8 0
The result is
x^2 - 2x - 8 = 0 which factors.
(x + 2)(x - 4) = 0
Answer
The factors are (x + 2)(x - 4)(x + 5)(x - 5) = 0
Long division
x^2 + 0 + 25 ||x^4 - 2x^3 - 33x^2 + 50x + 200 ||x^2 - 2x - 8
x^4 + 0 + 25x^2
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-2x^3 -8x^2 + 50x
-2x^3 + 0 + 50x
=================
-8x^2 + 0 +200
-8x^2 + 0 + 200
==================
0
No, 12/15 is less than 12/14
Area = π x radius²
dA/dr = 2πr
Average rate of change = (rate of change at one instant + rate of change at other instant)/2
= (2πr₁ + 2πr₂)/2
= (r₁ + r₂)π
Ai) 9π
Aii) 8.5π
Aiii) 8.1π
B) Instantaneous change:
(dA/dr) at (r = 4) = 2π(4)
= 8π
A rational number is<em> a number which can be written a ratio of two integers</em>.
In decimal form, a rational number is any number which either <em>terminates </em>or <em>repeats</em> after the decimal point. Since -1.987 terminates after the 7, it <em>is</em> a rational number.
