Factoring Polynomials
Definition of Factoring a Polynomial
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 x2 + 5x, means to write it as a product of
polynomials: x2 + 5x = x(x + 5).
We say x(x + 5) is the factorization of x2 + 5x.
| Multiply |
Factor |
|
3 · 5
2 · 3 · 3
5x(6x + 7)
(w + 6)(w - 5) |
= 15 = 18
= 30x2 + 35x
= w2 + w - 30 |
15
18
30x2 + 35x
w2 + w - 30 |
= 3 · 5
= 2 · 3 · 3
= 5x(6x + 7)
= (w + 6)(w - 5) |
|
