Explanation:
Factoring to linear factors generally involves finding the roots of the polynomial.
The two rules that are taught in Algebra courses for finding real roots of polynomials are ...
- Descartes' rule of signs: the number of positive real roots is equal to the number of coefficient sign changes when the polynomial is written in standard form.
- Rational root theorem: possible rational roots will have a numerator magnitude that is a divisor of the constant, and a denominator magnitude that is a divisor of the leading coefficient when the coefficients of the polynomial are rational. (Trial and error will narrow the selection.)
In general, it is a difficult problem to find irrational real factors, and even more difficult to find complex factors. The methods for finding complex factors are not generally taught in beginning Algebra courses, but may be taught in some numerical analysis courses.
Formulas exist for finding the roots of quadratic, cubic, and quartic polynomials. Above 2nd degree, they tend to be difficult to use, and may produce results that are less than easy to use. (The real roots of a cubic may be expressed in terms of cube roots of a complex number, for example.)
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Personally, I find a graphing calculator to be exceptionally useful for finding real roots. A suitable calculator can find irrational roots to calculator precision, and can use that capability to find a pair of complex roots if there is only one such pair.
There are web apps that will find all roots of virtually any polynomial of interest.
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<em>Additional comment</em>
Some algebra courses teach iterative methods for finding real zeros. These can include secant methods, bisection, and Newton's method iteration. There are anomalous cases that make use of these methods somewhat difficult, but they generally can work well if an approximate root value can be found.
Answer:
The height of the giraffe is 27.432 decimeters.
Step-by-step explanation:
To convert 1 foot to decimeters you would multiply by 3.048.
We need to multiply 9 feet by 3.048 which would give you the answer of 27.432 decimeters.
The width of the insect is 0.17 cm and the height of the insect is 0.125 cm.
Step-by-step explanation:
Step 1:
The scale factor is given by dividing the measurement after scaling by the same measurement
The given drawing of the insect is larger than the actual insect.
The scale factor is 20: 1 which means 20 cm on the drawing is 1 cm on the actual insect.
Step 2:
To obtain the actual insect's dimensions, we divide the dimensions of the drawing by 20.
The width of the actual insect 
The height of the actual insect 
The width of the insect is 0.17 cm and the height of the insect is 0.125 cm.
Answer:
21/2
Step-by-step explanation:
The answer can be determined by substracting the lengrh of the woodland trail from the Marsh trail
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converting the fraction to its simplest form gives 21/2
