Factor 2x squared minus 5x minus 3.
To factor a quadratic expression like 2x^2 - 5x - 3, you need to find two numbers that multiply to give you the product of the coefficient of the squared term (2) and the constant term (-3), and add up to the coefficient of the linear term (-5).
In this case, the coefficient of the squared term is 2, and the constant term is -3. We need to find two numbers that multiply to give -6 (2 multiplied by -3), and add up to -5.
To find these numbers, we can list the factors of -6 and check which pair adds up to -5.
Factors of -6: 1, -1, 2, -2, 3, -3, 6, -6
Out of these factors, the pair that adds up to -5 is 1 and -6.
Now, we can rewrite the middle term (-5x) as the sum of these two terms: -5x = 1x - 6x.
Putting it all together, we can factor the expression as:
2x^2 - 5x - 3 = 2x^2 + x - 6x - 3
= x(2x + 1) - 3(2x + 1)
= (2x + 1)(x - 3)
So the factored form of 2x^2 - 5x - 3 is (2x + 1)(x - 3).
Here we see that the x² term has a coefficient of 2, so the factorized form will be (x±?)(2x±?).
From the constant term of -3, we know that the factorized expression can only be (?x±1)(?x±3).
A couple of tries will give the correct answer, noting that the middle term is -5x:
2x²-5x-3
=(2x+1)(x-3)