SOLUTION: Can anyone offer steps and solution for this one? Factor each polynomial. If the polynomial is prime, say so. 18z + 45 + zē

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Can anyone offer steps and solution for this one? Factor each polynomial. If the polynomial is prime, say so. 18z + 45 + zē       Log On


   

Question 43872: Can anyone offer steps and solution for this one?

Factor each polynomial. If the polynomial is prime, say so.


18z + 45 + zē
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let's see if the expression can be factored. Rewrite it in standard form:
z%5E2%2B18z%2B45
The factors will look like: (z+a)(z+b) and you would like to have:
a*b = 45 and
a+b = 18
The factors of the first term are z%2Az+=+z%5E2
The possible factors (a & b) of the last term are:
3*15 = 45
5*9 = 45
Now you want the factors (a & b) of the last term to add up to 18 (a+b = 18) so you can get the middle term of your original expression (18z).
It looks like 3+15 = 18, so a = 3 and b = 15
So the factors of:
z%5E2%2B18z%2B45+=+%28z%2B3%29%28z%2B15%29