The Big Idea: Factoring is unmultiplying.
Example $$8 x t^{3}-20 x^{4} t^{2}=4xt^{2}(2t-5x^{3})$$
Finding the GCF
The GCF of a polynomial is the collection of all common factors of every term.
Example: Find the GCF of $8 x t^{3}-20 x^{4} t^{2}$.
Examples: Find the GCF of each polynomial and factor it out.
$8 x t^{3}-20 x^{4} t^{2}$
$6 \gamma^{2}+12 \gamma^{3}+10 \gamma$
$12a^3 b - 18a^2 b^2 + 30ab^3$
$(12 \phi-8) (16 a) + (12 \phi-8) (20 x)$
Factoring By Grouping: Polynomials with 4 terms are often factored by grouping.
Examples
$35 c s+21 s+10 c r+6 r$
$21 u w-35 w+18 u t-30 t$
Question: Will any grouping lead us to the correct factorization?
Grumpy Cat Answer:
Example : We may need to rearrange some terms before we can apply factoring by grouping.
$6 a \beta-35 v y+15 \beta y-14 a v$