Question

Factor this linear expression :7x- 3

Answer 1

Recall the distributive property of real numbers:

`ac+bc=c\cdot(a+b)`

Analyze each expression in order to check if the terms have common factors and use the distributive property to rewrite each expression.

a) The gcf of 15 and 10 is 5, since 15=5*3 and 10=5*2. Then:

`15x+10=5\cdot3x+5\cdot2=5(3x+2)`

b) The gcf of 7 and 3 is 1. Then, the expression will remain the same if we factor out 1:

`7x-3=1\cdot7x-1\cdot3=1(7x-3)=7x-3`

c) The gcf of 6 and 9 is 3, since 3*2=6 and 3*3=9. Then:

`6x+9=3\cdot2x+3\cdot3=3\cdot(2x+3)`

d) The gcf of 30 and 25 is 5 since 5*6=30 and 5*5=25. Then:

`30x-25=5\cdot6x-5\cdot5=5\cdot(6x-5)`