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

Jun 12, 2018

Yes
$\left(x + 4\right) \times \left(x - 1\right)$

#### 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} = ${x}^{2} + 3 x - 4$

Now the x terms are in the standard $A {x}^{2} + B x + C$

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 $2 \times 2$ and $4 \times 1$

$4 - 1 = 3$

The binomial factors then are

$\left(x + 4\right) \times \left(x - 1\right)$