# How do you factor the polynomials 3dt-21d+35-5t?

Jan 6, 2017

$= \left(t - 7\right) \left(3 d - 5\right)$

#### Explanation:

The number of terms is a good clue as to the type of factorising which can be done. There is no common factor in all the terms, but we can group them into pairs:

$\left(3 \mathrm{dt} - 21 d\right) + \left(35 - 5 t\right) \text{ } \leftarrow$ take out common factors

=3d(t-7) color(blue)(+ 5(" "7-t))" "larr do a sign switch round
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots . \ldots . .} \downarrow \textcolor{w h i t e}{.} \downarrow \textcolor{w h i t e}{.} \downarrow$
$= 3 d \left(t - 7\right) \textcolor{b l u e}{- 5 \left(- 7 + t\right)}$

$= 3 d \left(t - 7\right) - \textcolor{b l u e}{5 \left(t - 7\right)} \text{ } \leftarrow$ common bracket

$= \left(t - 7\right) \left(3 d - 5\right)$