factor the basic trinomial:
3x^2 + 21x +30
To factor the trinomial 3x^2 + 21x + 30, we first need to find the greatest common factor of all the terms, which is 3.
Dividing each term by 3, we get:
3x^2/3 + 21x/3 + 30/3
x^2 + 7x + 10
Now we need to factor the trinomial x^2 + 7x + 10. This can be factored into two binomials as:
(x + 5)(x + 2)
Therefore, the factored form of the trinomial 3x^2 + 21x + 30 is:
3(x + 5)(x + 2)