Question

What is the factored form of
2x^2 + x -3
Please explain the answer

Answer 1

To factor the trinomial 2x^2 + x - 3, we need to find two numbers that multiply to -6 (the product of the coefficient of x^2 and the constant term) and add to +1 (the coefficient of x).

The two numbers that meet these conditions are +3 and -2 because:
3 * -2 = -6
3 + (-2) = 1

Now we rewrite the middle term using these two numbers:
2x^2 + 3x - 2x - 3

Factor by grouping:
2x(x + 3) - 1(x + 3)

Now we factor out the common factor, (x + 3):
(x + 3)(2x - 1)

Therefore, the factored form of 2x^2 + x - 3 is (x + 3)(2x - 1).