# What is factorization in algebra 1

## Meinstein

Factoring or factorization of polynomials in algebra is understood as the decomposition of polynomials into a product of polynomials (expressions) that can no longer be decomposed, as is the case with the prime factorization of whole numbers.

Work according to the following grid:

- Can a common factor be written in front of the brackets?
- Is it a binomial formula?
- Is it a binomial-like formula (3 terms, one square)?
- Can you make progress with forming a group (often a sum of four summands)?
- Am I done or can a term be factored further?

### Examples

1.

m (r - s) - n (s - r) =

m (r - s) + n (r - s) = we multiply the second bracket by -1

(r - s) (m + n) we exclude.

2.

-4s + 8t + t - 10s - 5t =

s (- 4 - 10) + t (8 + 1 - 5 =

- 14s + 4t

### Exercises

- 24a
^{4}- 32a^{3}= - 39a
^{2}n^{2}- 26an = - −20m + 12n - 4q =
- 10am - 6an - 2ap =
- 7a
^{2}b - 21ab^{2}+ from = - - ac - bc - c =
- y
^{3}- y2 = - 2a
^{3}bc + 8a^{2}b^{2}c - 2ab^{3}c - 2a^{2}bc^{2}+ 16abc^{3}= - −6x
^{4}y^{4}z^{4}+ 18x^{3}y^{3}z^{3}- 12x^{2}y^{2}z^{3}= - 36m
^{5}n^{6}- 90m^{4}n^{7}- 180m^{3}n^{8}=

Solutions:

8a^{3} (3a - 4)

13an (3an - 2)

- 4 (5m - 3n + q)

It is better here to factor out -4; Be careful with the signs!

2a (5m - 3n - p)

Don't forget the 1!

from (7a - 21b + 1)

c (a + b + 1)

y^{2} (y - 1)

Perhaps as a precaution, write the terms one below the other:

2abc (a^{2} + 4ab - b^{2} - ac + 8c^{2})

2a3

bc + 8a2b2c - 2ab3

c - 2a2

bc2 + 16abc3 =

2abc (a2 + 4ab - b2 - ac + 8c2)

9

Be selective about the term that you put in front of the parentheses:

first consider only the existing numbers, then the x, then the y, then the z.

−6x 4y4z4 + 18 × 3 y3 z3 - 12x2y2z3 = −6 × 2 y2 z3 (x2 y2 z - 3xy + 2)

10 36m5n6 - 90m4n7 - 180m3n8 = 18m3n6 (2m2 - 5mn - 10n2)

### Similar issues

Prime numbers

Prime factorization

Factoring trinomials

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