2x^2-x-3
Is there an equals sign? Or doesn't it matter?
Factor this trinomial.
2x^2-x-3 Factor this trinomial.
I recommend use of the AC or "Amazing" method.
a=2, b=-1, c=-3
a*c=-6 We need to find factors of a*c that sum to b
factors sum
-6 1 -5
-3 2 -1 this is it
take those factors and use as denominators with a as numerator. Reduce to simplest terms. leave negative signs where they started. You now have coefficients.
2/-3 -> 2x-3
2/2=1/1 --> x+1
2x^2-x-3=(2x-3)(x+1)
The expression 2x^2 - x - 3 is a quadratic expression, meaning it is a polynomial of degree 2. To work with quadratic expressions, we can apply various methods such as factoring, completing the square, or using the quadratic formula.
To factor the quadratic expression, we need to write it as a product of two binomial expressions. However, this expression is not easily factorable by factoring using integer values. In such cases, we can resort to factoring using the quadratic formula.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the expression 2x^2 - x - 3, the coefficients are:
a = 2, b = -1, and c = -3.
Substituting these values into the quadratic formula, we can solve for x:
x = (-(-1) ± √((-1)^2 - 4 * 2 * (-3))) / (2 * 2)
Simplifying the equation further:
x = (1 ± √(1 + 24)) / 4
x = (1 ± √25) / 4
x = (1 ± 5) / 4
This gives us two solutions:
x1 = (1 + 5) / 4 = 6 / 4 = 3/2
x2 = (1 - 5) / 4 = -4 / 4 = -1
Therefore, the solutions to the quadratic expression 2x^2 - x - 3 are x = 3/2 and x = -1.