(2x^2 + 10x + 12) divided by (x + 3)
your question is
(2x^2 + 10x + 12)/(x + 3)
=2(x+2)(x+3)/(x+3)
=
can you take it from here?
Certainly! To simplify the expression (2x^2 + 10x + 12)/(x + 3), we can factor the numerator and cancel out common terms with the denominator.
Step 1: Factor the numerator (2x^2 + 10x + 12):
The expression can be factored as follows:
2x^2 + 10x + 12 = 2(x^2 + 5x + 6)
To factor the quadratic expression within the parentheses, we need to find two numbers that multiply to give 6 and add up to 5. The numbers 2 and 3 satisfy these conditions:
x^2 + 5x + 6 = (x + 2)(x + 3)
So, the factored form of the numerator becomes:
2(x + 2)(x + 3)
Step 2: Cancel out common terms:
Now, we can cancel out the common factor of (x + 3) in the numerator and denominator:
(2(x + 2)(x + 3))/(x + 3) = 2(x + 2)
Therefore, the simplified expression is 2(x + 2).
Please note that canceling out common factors is only valid when the denominator is not zero. In this case, we assume x + 3 is not equal to zero, which means x ≠ -3.