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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.
To learn more on polynomials: brainly.com/question/11536910
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The motion of the rock thrown from the cliff which goes downwards due to
the gravitational force, is a free fall motion.
- 125 represents; <u>A. The initial height of the rock</u>.
Reasons:
The given function that represents the height of the of the rock in feet <em>x</em> seconds after being thrown is; f(x) = 16·x² + 4·x + 125
At the initial height before being thrown from the cliff, we have;
The time, x = 0
The initial height is therefore;
The initial height f(0) = 16 × (0)² + 4 × (0) + 125 = 125
125 represents <u>A. The initial height of the rock</u>
Learn more about motion under gravity here:
brainly.com/question/7596138
