Question

How do you factor `3x^2 + 28x + 32`?

Answer 1

`(3x+4)(x+8)`

Explanation:

`3x^2 +28x +32`

Find factors of 32 which ADD to make 28.
The signs are the same both positive

As 3 isa prime number, its only factors are 3 and 1.

As a start, ask what factors of 32 can we use to get to just less than 28. (we still have to ADD on something...)

`3xx8 = 24` seems a possible start.
Choose factors and cross-mulitply

`color(white)(xxx)3color(white)(xxx)32`

`color(white)(xxx)3color(white)(xxxx)4 " "rarr 1xx4 =4`
`color(white)(xxx)1color(white)(xxxx)8" "rarr3xx8 = ul24`
`color(white)(xxxxxxxxxxxxxxxxxxxx)28`

`(3x+4)(x+8)`