Factor the following trinomial:
12x^2 - 11x + 2
Please help I have no idea how to do this!
12x2 = 24
look for two numbers which multiply to get 24 and have a sum of -11
how about -3 and -8
so 12x^2 - 11x + 2
= 12x^2 - 3x - 8x + 2
= 3x(4x - 1) - 2(4x - 1)
= (4x-1)(3x-2)
thanks
To factor a trinomial, we need to find two binomials such that when multiplied together, they give us the original trinomial.
In this case, we have the trinomial:
12x^2 - 11x + 2
To factor it, we start by looking at the coefficient of the first term, which is 12. We then look at the constant term, which is 2.
Next, we need to find two numbers that multiply to give us the product of the coefficient of the first term (12) and the constant term (2), and that add up to give us the coefficient of the middle term (-11). In this case, the two numbers are -1 and -2.
Now we can rewrite the middle term (-11x) using -1x and -2x:
12x^2 - 1x - 2x + 2
Now, we can group the terms and factor by grouping:
(12x^2 - 1x) + (-2x + 2)
Taking out the common factors from each group, we have:
x(12x - 1) - 2(12x - 1)
We now have a common binomial factor, (12x - 1), which we can factor out:
(12x - 1)(x - 2)
Therefore, the trinomial 12x^2 - 11x + 2 can be factored as (12x - 1)(x - 2).