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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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8y-2(y+4)= i was just wondering the best way to work this
Bond [772]

Answer:

6y-8

Step-by-step explanation:

8y-2(y+4)

8y-2y-8 distribution

6y-8 combined like-terms

4 0
3 years ago
How do you solve 145 times 23
liq [111]

Answer:

3335

Step-by-step explanation:

You basically add 145 together 23 times

6 0
2 years ago
What is the greatest value 20g of flour 3 for 3.50 or 40g of flour for 2 for 9£ which is better for money
jenyasd209 [6]

Answer:

It is better to buy 20 g of flour 3 for 3.50

Step-by-step explanation:

It is given that 20g of 3 for 3.50

It means 3 packets of 20 g is 3*20 =60

So, 60g  is for 3.50

So, 1 g =\frac{3.5}{60}=0.05833 per gram.

Now, let's find unit rate for 40 g of 2 for 9.

2 packets of 40 gram = 2* 40 =80 grams

So, 80 grams costs 9

So, 1 gram =\frac{9}{80} =0.1125

So, it is better to buy 20 g of flour 3 for 3.50

4 0
2 years ago
How many planes of symmetry does a rectangular pyramid has?<br>​
Tju [1.3M]

Answer:

6

Step-by-step explanation:

6 0
2 years ago
Jenny's bakery sells carrot muffins at 2 dollars each. The electricity to run the over is over 120 dollars per day and the cost
g100num [7]

Answer:

200 muffins

Step-by-step explanation:

The selling price of each muffin = $2

The cost price of each muffin = $1.40

The price of electricity = $120

If the number of muffins that Jenny sells in a day is x, then, Jenny's total cost in a day is:

120 + (1.4 * x) = 120 + 1.4x

and the total sales earnings in a day for x muffins will be:

2 * x = 2x

To break even, the total costs in a day must equal to the total earnings. That is;

2x =  120 + 1.4x

Solving this:

2x - 1.4x = 120\\\\\\0.6x = 120\\\\\\x = 120/0.6\\\\\\x = 200

She must sell 200 muffins in a day to break even.

7 0
3 years ago
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