how to factorise f(z)= z^2 +4z+7
To factorize the expression f(z) = z^2 + 4z + 7, we need to find two numbers that multiply to 7 and add up to 4. The two numbers that satisfy this condition are 1 and 7.
So, we can rewrite the expression as:
f(z) = z^2 + 4z + 7
= z^2 + z + 3z + 7
= z(z + 1) + 1(3z + 7)
Therefore, the factorized form of f(z) = z^2 + 4z + 7 is (z + 1)(z + 7).