Please help with the following:
Factor completely
3x^2-5x+1
i don't think this is factorable try using the quadratic equation
The factors are irrational. Use the quadratic equation.
To factor a quadratic expression completely, we need to find two binomial factors that, when multiplied, give us the original expression.
Given the quadratic expression: 3x^2 - 5x + 1
To factor it, we need to find two numbers that multiply to give us the product of the coefficient of x^2 (which is 3) and the constant term (which is 1) and at the same time, add up to give us the coefficient of x (which is -5).
Let's break it down:
The coefficient of x^2 is 3.
The constant term is 1.
The product of these coefficients is 3 * 1 = 3.
Now, we need to find two numbers whose product is 3 and whose sum is -5.
After some trial and error, we can find that: -3 and -2 meet the criteria.
Therefore, we can rewrite the quadratic expression with the help of these two numbers:
3x^2 - 3x - 2x + 1
Now, we group the terms:
(3x^2 - 3x) + (-2x + 1)
We can factor out the greatest common factor from each group:
3x(x - 1) - 1(2x - 1)
Finally, we have factored the expression completely:
(3x - 1)(x - 1)