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

1 Answer
Jun 12, 2018

Answer:

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) #