Answer:
E. x = 3
Step-by-step explanation:
The equation can be factored by considering the factors of the product of the first and last coefficients. Those factors must have a sum equal to the middle coefficient.
(2)(-3) = -6 = (-6)(1) = (-3)(2) = ... other factors with positive sums
The sums of the factor pairs shown are -5 and -1. We're interested in the factor pair {-6, 1}. Replacing the middle term coefficient with the sum of these, we can write the equation in a way that lets us factor pairs of terms.
2x² -6x +x -3 = 0 . . . . . . . . replace -5x with -6x+1x
2x(x -3) +1(x -3) = 0 . . . . . . factor pairs of terms
(2x +1)(x -3) = 0 . . . . . . . . . complete the factoring
Solutions are the values of x that make these factors zero:
2x +1 = 0 ⇒ x = -1/2
x -3 = 0 ⇒ x = 3
_____
Additional comment
A number of methods are used to find the factors of a quadratic with a leading coefficient other than 1. When the coefficients are small integers, this is one of the more straightforward methods: actually listing and examining the pairs of factors of "ac." If "ac" has a large number of divisors, other methods may be more practical.
