What is the best way to factor a polynomial?

Question

I get confused when I have to factor polynomials. What's the best way to do it without having to guess a lot about what the factors are?

Answer 1

The best possible way to factorize a given polynomial depends upon the type of polynomial.

 

 

If the polynomial is simple enough, and is given in standard forms of the following types, (a² - b²), (a³ - b³), or (a³ + b³), then you can use the following formulas to factor it:

 

(a² - b²) = (a+b)(a-b)

(a³ - b3) = (a-b)(a² + ab + b²)

(a³ + b³) = (a+b)(a² - ab - b²)

 

 

For a quadratic equation in the form of ax² + bx + c = 0; you can use the quadratic formula to find the roots.

 

The formula for the roots is given as: x = { -b ± √(b² - 4ac) } / 2a

Substituting the value of the coefficients in the above equation, the roots will be easy to find.

Answer 2

The best way is to use the quadratic formula.  In a quadratic equation, the standard form is

 

ax² + bx + c = 0

 

where  a, b, and c are coefficients.

 

 

So the quadratic formula is

 

x = (-b ± √(b² - 4ac)) / 2a

 

 

The plus/minus sign tells us that we will have two solutions for x.  They are

 

x = (-b + √(b² - 4ac)) / 2a              and              x = (-b - √(b² - 4ac)) / 2a

 

 

Once you have the values of x, you put them in factor form.  For example, if one solution is

 

x = 2  ,

 

then the factored form is

 

(x - 2)

Answer 3

Follow this list:

Factor Greatest Common Factor (if any)

Look for one of the General Forms

Use FOIL

 

Now about "guessing" the factors, that can be mitigated by having an excellent working knowledge of the multiplication tables. Try that!