Factoring by Grouping (Part 2)

Factoring by Grouping (Part 2)

How to factor polynomials by grouping and using other formulas together: examples and their solutions.

Example 1

Factor the given polynomial. xy^2 - xz^2 + y^2 - z^2

Polynomials that cannot be factored by using formulas
can mostly be solved by grouping.

Factoring by grouping (part 1)

Split the polynomial into two parts.

Factor the first two terms:
x(y2 - z2).

The next two terms are already set:
(y2 - z2).

Factor the polynomial by using the common factor:
(y2 - z2).

Factor the available factors thoroughly.

y2 - z2 = (y + z)(y - z)

Factoring the difference of squares

Example 2

Factor the given polynomial. a^3 + 2a^2 - 3a - 2a^2b - 4ab + 6b

Split the polynomial into two parts.

Factor the first three terms:
a(a2 + 2a - 3).

Factor the next three terms
with making (a2 + 2a - 3):
-2b(a2 + 2a - 3).

Factor the polynomial by using the common factor:
(a2 + 2a - 3).

Factor the available factors thoroughly.

a2 + 2a - 3 = (a + 3)(a - 1)

Factoring a quadratic trinomial