Question

solve the equation by factoring. (z^2 - z - 6 = 0) a. z = –2 or z = 3 b. z = 2 or z = 3 c. z = –2 or z = –3 d. z = 2 or z = –3. (50 POINTS PLEASE HELP)

Answer 1

Answer:

Answer is below

Step-by-step explanation:

Factor left side of equation.

$(z+2)(z-3)=0$

Set factors equal to 0.

$z+2=0 or z-3=0\\\\z=-2 \\Or\\ z=3$

Answer 2

Answer: (z + 2)(z - 3)

Step-by-step explanation:

First, we have 1 as a coefficient on z², so we multiply that by -6, which gives us -6. Now we must find out what two numbers when multiplied, give us -6, and when added together, give us -1 (z's coefficient). Going through -6's factors, I got -3 and 2 since we need a negative one when they are added together. Now we can input our values:

(z - 3)(z + 2).

Double checking, we get the starting equation, which means our factorization was correct, and so is the solution.

Note: it does not matter which binomial comes first because you will get the same answer regardless of its position.