Question

Find the zeros of the following expression x^2+5x+6 show all work

Answer 1

Let y = 0 to find the zeros.
$x^{2} + 5x + 6 = 0$

We can now split the middle term into factors of 6 that add up to 5.
$x^{2} + 3x + 2x + 6 = 0$

Group the first two terms, and group the last two terms, and factorise.
$(x^{2} + 3x) + (2x + 6) = 0$
$x(x + 3) + 2(x + 3) = 0$

Group like terms.
$(x + 3)(x + 2) = 0$

Now, we know that in order for a zero to occur, either x + 3 = 0 or x + 2 = 0.
Hence, x = -3 and -2 are the zeros in this quadratic.