The <em>least</em> polynomial in <em>standard</em> form is defined by the function f(x) = x⁷ + 6 · x⁶ - 54 · x⁴ - 81 · x³.
<h3>How to determine the least polynomial given a set of roots and a leading coefficient</h3>
Polynomials can be expressed as a product of binomials of the form (x - r) multiplied by a <em>leading</em> coefficient. The <em>least</em> polynomial contain the number of roots presented in statement, whose <em>factor</em> form is shown below:
f(x) = 1 · (x + 3)³ · x³ · (x - 3)
f(x) = (x + 3)³ · (x⁴ - 3 · x³)
f(x) = (x³ + 9 · x² + 27 · x + 27) · (x⁴ - 3 · x³)
f(x) = x⁷ + 9 · x⁶ + 27 · x⁵ + 27 · x⁴ - 3 · x⁶ - 27 · x⁵ - 81 · x⁴ - 81 · x³
f(x) = x⁷ + 6 · x⁶ - 54 · x⁴ - 81 · x³
The <em>least</em> polynomial in <em>standard</em> form is defined by the function f(x) = x⁷ + 6 · x⁶ - 54 · x⁴ - 81 · x³.
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<h3>
Answer: Choice D</h3>
Explanation:
Start at the arrow tip. Move vertically until reaching the x axis. You'll arrive at x = 7 which is the x component of the vector.
Go back to the arrow tip. This time move horizontally until reaching the y axis, so you should arrive at y = -6
Therefore the vector is which is in a column vector format. A row vector would have the numbers listed horizontally.
Put another way, the arrow tip is at the point location of (7,-6). This leads directly to the column vector mentioned in the previous paragraph.
A closed shape with straight sides
0 -18 is the answer to your question
F + 0.3 < 1.7
Subtract 0.3 on both sides
F < 1.4
Your final answer is F < 1.4