Question

How do you factor `3x^2-20x-7`?

Answer 1

`3x^2-20x-7=(3x+1)(x-7)`

Explanation:

For factorizing `ax^2+bx+c`, one needs to split `b` in two parts whose products is `ac`. As such in `3x^2-20x-7`, one needs to split `-20` in two parts whose product is `3×(-7)=-21` i.e. `-21` and `1`. Hence,

`3x^2-20x-7`

= `3x^2-21x+x-7` or

= `3x(x-7)+1(x-7)` or

= `(3x+1)(x-7)`

Answer 2

`(3x+1)(x-7)`

Explanation:

Factoring this expression is easier than others, because both 3 and 7 are prime numbers, which reduces the number of cross products to only 2 possibilities...

3 with 7 and 1 with 1, or 3 with 1 and 7 with 1.

The - sign in front of the 7 tells us we need to SUBTRACT the factors.

The coefficient of x which is 20 tells us what answer we need from the subtraction.

"Find factors of 3 and 7 which SUBTRACT to give 20"

Find the cross product

`" 3 + 1 " rArr 1xx+1 = +1`
`" 1 -7 "rArr 3 xx -7= -21" "( -21 +1 = -20)`

The top row is the first bracket, the bottom is the second.

`(3x+1)(x-7)`