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To factor means to write a quantity or an expression as a product.

To factor a whole number, such as 12, we write it as a product of whole numbers. For example:

12 = 2 · 6

12 = 2 · 2 · 3

To factor a polynomial, such as x^{2} + 5x, means to write it as a product of polynomials: x^{2} + 5x = x(x + 5).

We say x(x + 5) is the factorization of x^{2} + 5x.

3 · 5

2 · 3 · 3

5x(6x + 7)

(w + 6)(w - 5)

= 18

= 30x^{2} + 35x

= w^{2} + w - 30

15

18

30x^{2} + 35x

w^{2} + w - 30

= 2 · 3 · 3

= 5x(6x + 7)

= (w + 6)(w - 5)