5k^2 - 39k + 54 Factor the trinomial using the ac-method

Answer 1

To factor the trinomial using the AC-method, we need to find two numbers whose product is equal to the product of the first and last term in the trinomial (product of 5k^2 and 54) and whose sum is equal to the coefficient of the middle term (-39k).

The product of 5k^2 and 54 is 270k^2.

Now, we need to find two numbers whose product is 270k^2 and whose sum is -39k.

The numbers that satisfy these conditions are -15k and -18k, because (-15k)(-18k) = 270k^2 and (-15k) + (-18k) = -33k.

Now we can rewrite the original trinomial:

5k^2 - 39k + 54 = 5k^2 - 15k - 18k + 54

Then we group the terms:

(5k^2 - 15k) + (-18k + 54)

Now, we can factor out the greatest common factor from each group:

5k(k - 3) - 18(k - 3)

Notice that now we have a common binomial factor of (k - 3) in each term.

So, we can factor out (k - 3):

(k - 3)(5k - 18)

Therefore, the trinomial 5k^2 - 39k + 54 is factored as (k - 3)(5k - 18).