What is the factorization of the quadratic expression 3x2+5x−23𝑥2+5𝑥−2 ?
To factorize the quadratic expression 3x^2 + 5x - 2, we need to find two numbers that multiply to -6 (the product of the coefficient of x^2 term and the constant term) and add up to the coefficient of the x term (5).
The numbers that satisfy these conditions are 6 and -1. So, we can rewrite the expression as:
3x^2 + 6x - x - 2
Now, we can factor by grouping:
3x(x + 2) - 1(x + 2)
Now, we can factor out the common factor of (x + 2):
(x + 2)(3x - 1)
Therefore, the factorization of the quadratic expression 3x^2 + 5x - 2 is (x + 2)(3x - 1).