Factor 3y^2-42y+144
To factor the expression 3y^2 - 42y + 144, we can start by finding the greatest common factor (GCF) of all the terms.
The GCF of 3y^2, -42y, and 144 is 3.
Dividing each term by the GCF 3, we get:
3y^2/3 - 42y/3 + 144/3
= y^2 - 14y + 48
Now, we need to factor the trinomial y^2 - 14y + 48.
Looking at the coefficient of y^2, which is 1, we need to find two numbers that multiply to give 48 (the constant term) and add up to -14 (the coefficient of y).
The numbers that fit this criteria are -6 and -8.
Therefore, we can rewrite the expression as:
(y - 6)(y - 8).
So, the factored form of 3y^2 - 42y + 144 is (y - 6)(y - 8).