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katrin2010 [14]
2 years ago
7

How to factor a tri, quad, or polynomial.

Mathematics
1 answer:
Akimi4 [234]2 years ago
6 0

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.)

__

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.

_____

<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.

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PLEASE HELP ASAP!!
Art [367]

Answer:

See explanation

Step-by-step explanation:

A.  P(top)=top outcomes/all kinds of outcomes=4/30=2/15=13.33333333333...%

P(bottom)=bottom outcomes/ all kinds of outcomes=1/30=3.33333333....%

P(side)=25/30=5/6=83.33333333333...%

B. No. If were equally likely, the probabilities for A would have been roughly the same. It seems like the side event is more probable.

7 0
3 years ago
What is lim x→-3 sqrt x^2-8
vitfil [10]

If the  -8 is under the square root, then...

\displaystyle L = \lim_{x\to -3} \sqrt{x^2-8}\\\\L = \sqrt{(-3)^2-8}\\\\L = \sqrt{9-8}\\\\L = \sqrt{1}\\\\L = 1\\\\

OR

If the -8 is not under the square root, then...

\displaystyle L = \lim_{x\to -3} \sqrt{x^2}-8\\\\L = \sqrt{(-3)^2}-8\\\\L = \sqrt{9}-8\\\\L = 3-8\\\\L = -5

Either way, we replace x with -3 and simplify.

For more information, refer to the direct substitution rule for limits.

4 0
1 year ago
A certain number exceeds 18 by as much as 44 exceed the number. What is the number?
asambeis [7]

Answer:

x=31  is the required number.

Step-by-step explanation:

Let the number be represented as "x".

Then, According to the statement given, "x" exceeds by as much as 44 exceed the number, then the equation can be written as:

⇒x-18=44-x

⇒x+x=44+18

⇒2x=62

⇒x=31

Hence, the required number is x =31.

5 0
3 years ago
I’m still confused on how to work the percentages
Serjik [45]

Answer:

13 is your answer

Step-by-step explanation:

it's the biggest number and more students like cats

Hope this helps

God bless you

Have a great day

- Kayla :)

5 0
3 years ago
Read 2 more answers
Help me please fast fast fast
vova2212 [387]

4

You can just put this into a calculator:

1/2^2 = 0.25

3×5-3 = 12

1^3 = 1

0.25 × 12 + 1 = 4

4 0
2 years ago
Read 2 more answers
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