factorize completely
12x squared -23x +5
Use the AC method for factoring:
(-4x+1)(-3x+5)
Hope it helps!
or
(4x - 1)(3x - 5)
looks "nicer"
To factorize the quadratic expression completely, we need to find two binomial factors that multiply together to give the original expression. Let's break down the steps to factorize the expression:
1. The expression is in the form of ax^2 + bx + c, where a = 12, b = -23, and c = 5.
2. To factorize the expression, we need to find two numbers that multiply together to give ac (product of a and c) and add up to b.
In this case, ac = 12 * 5 = 60. We need to find two numbers whose product is 60 and sum is -23.
3. After some trial and error, we can determine that the numbers are -20 and -3. (-20 * -3 = 60 and -20 + (-3) = -23)
4. Now, we can rewrite the middle term (-23x) of the quadratic expression using the two numbers we found:
-23x can be written as -20x - 3x.
5. Next, we group the terms and factor by grouping:
12x^2 - 20x - 3x + 5
Taking common factors from the first two terms and the last two terms, we get:
4x(3x - 5) - 1(3x - 5)
6. Notice that we have a common binomial factor of (3x - 5). We can factor this out:
(3x - 5)(4x - 1)
Thus, the completely factored form of the expression 12x^2 - 23x + 5 is (3x - 5)(4x - 1).