Question

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

Answer 1

`=(t-7)(3d-5)`

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:

`(3dt -21d) + (35-5t)" "larr` take out common factors

`=3d(t-7) color(blue)(+ 5(" "7-t))" "larr` do a sign switch round
`color(white)(............. .....)darrcolor(white)(.)darrcolor(white)(.)darr`
`=3d(t-7) color(blue)(- 5(-7+t))`

`=3d(t-7)- color(blue)(5(t-7))" "larr` common bracket

`=(t-7)(3d-5)`