Question

Is it possible to factor `y= 1/2x^2 + 3/2x -4`? If so, what are the factors?

Answer 1

Yes
`( x +4) xx ( x -1)`

Explanation:

first consider y to be any number and its value not needed for the purpose of factoring

second multiply everything by 2

`2 { (1/2 x^2 + (3/2) x - 4}`= `x^2 + 3x -4`

Now the x terms are in the standard `Ax^2 + Bx + C`

Since the C is -4 one binomial factor must be negative and the other binomial factor must be positive.

The B is +3 which means the positive binomial factor must be greater than the the negative binomial factor.

third used the information given by the B and C values to find the binomial factors.

The only factors of 4 are `2 xx 2` and `4 xx 1`

`4- 1 = 3`

The binomial factors then are

`( x +4) xx ( x -1)`