factor the following expression.\n2z² - 7z - 15\n(2z + ?)(z - )

Explanation:

Step1: Multiply leading - coefficient and constant

For the quadratic expression (ax^{2}+bx + c=2z^{2}-7z - 15), where (a = 2), (b=-7), (c=-15). Calculate (a\times c=2\times(-15)=-30).

Step2: Find two numbers

We need to find two numbers that multiply to (-30) and add up to (b=-7). The numbers are (3) and (-10) since (3\times(-10)=-30) and (3+( - 10)=-7).

Step3: Rewrite the middle term

Rewrite (-7z) as (3z-10z). So, (2z^{2}-7z - 15=2z^{2}+3z-10z - 15).

Step4: Group the terms

Group the terms: ((2z^{2}+3z)+(-10z - 15)).

Step5: Factor out the GCF from each group

Factor out the GCF from each group. From (2z^{2}+3z), the GCF is (z), so (2z^{2}+3z=z(2z + 3)). From (-10z - 15), the GCF is (-5), so (-10z - 15=-5(2z + 3)).

Step6: Factor out the common binomial factor

(z(2z + 3)-5(2z + 3)=(2z + 3)(z - 5))

Answer:

((2z + 3)(z - 5))