Method on @sym: e = factor (n) ¶

Method on @sym: [p, m] = factor (n) ¶

Method on @sym: g = factor (f) ¶

Method on @sym: g = factor (f, x) ¶

Method on @sym: g = factor (f, x, y, …) ¶

Factor a symbolic polynomial or integer.

A symbolic integer n can be factored:

e = factor(sym(28152))
  ⇒ e = (sym)
        1  3   1  2
      17 ⋅2 ⋅23 ⋅3

However, if you want to do anything other than just look at the result, you probably want:

[p, m] = factor(sym(28152))
  ⇒ p = (sym) [2  3  17  23]  (1×4 matrix)
  ⇒ m = (sym) [3  2  1  1]  (1×4 matrix)
prod(p.^m)
  ⇒ (sym) 28152

An example of factoring a polynomial:

syms x
factor(x^2 + 7*x + 12)
  ⇒ (sym) (x + 3)⋅(x + 4)

When the expression f depends on multiple variables, the second argument x effects what is factored:

syms x y
f = expand((x+3)*(x+4)*(y+5)*(y+6));
factor(f)
  ⇒ (sym) (x + 3)⋅(x + 4)⋅(y + 5)⋅(y + 6)
factor(f, x, y)
  ⇒ (sym) (x + 3)⋅(x + 4)⋅(y + 5)⋅(y + 6)
factor(f, x)
  ⇒ (sym)
                      ⎛ 2            ⎞
      (x + 3)⋅(x + 4)⋅⎝y  + 11⋅y + 30⎠
factor(f, y)
  ⇒ (sym)
                      ⎛ 2           ⎞
      (y + 5)⋅(y + 6)⋅⎝x  + 7⋅x + 12⎠

Passing input x can be useful if your expression f might be a constant and you wish to avoid factoring it as an integer:

f = sym(42);    % i.e., a degree-zero polynomial
factor(f)       % no, don't want this
  ⇒ (sym)
       1  1  1
      2 ⋅3 ⋅7
factor(f, x)
  ⇒ (sym) 42

See also: @@sym/expand.

Package: symbolic