SOLUTION: When 35z^2-23z-72 is factored completely, one of the factors is: a. (7z-9) b. (5z+8) c. (7z+9) d. (5z-9)

Algebra.Com
Question 131292: When 35z^2-23z-72 is factored completely, one of the factors is:
a. (7z-9)
b. (5z+8)
c. (7z+9)
d. (5z-9)
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is where the coefficients are 35 and -72 respectively.

Now multiply the first coefficient 35 and the last coefficient -72 to get -2520. Now what two numbers multiply to -2520 and add to the middle coefficient -23? Let's list all of the factors of -2520:



Factors of -2520:
1,2,3,4,5,6,7,8,9,10,12,14,15,18,20,21,24,28,30,35,36,40,42,45,56,60,63,70,72,84,90,105,120,126,140,168,180,210,252,280,315,360,420,504,630,840,1260,2520

-1,-2,-3,-4,-5,-6,-7,-8,-9,-10,-12,-14,-15,-18,-20,-21,-24,-28,-30,-35,-36,-40,-42,-45,-56,-60,-63,-70,-72,-84,-90,-105,-120,-126,-140,-168,-180,-210,-252,-280,-315,-360,-420,-504,-630,-840,-1260,-2520 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -2520
(1)*(-2520)
(2)*(-1260)
(3)*(-840)
(4)*(-630)
(5)*(-504)
(6)*(-420)
(7)*(-360)
(8)*(-315)
(9)*(-280)
(10)*(-252)
(12)*(-210)
(14)*(-180)
(15)*(-168)
(18)*(-140)
(20)*(-126)
(21)*(-120)
(24)*(-105)
(28)*(-90)
(30)*(-84)
(35)*(-72)
(36)*(-70)
(40)*(-63)
(42)*(-60)
(45)*(-56)
(-1)*(2520)
(-2)*(1260)
(-3)*(840)
(-4)*(630)
(-5)*(504)
(-6)*(420)
(-7)*(360)
(-8)*(315)
(-9)*(280)
(-10)*(252)
(-12)*(210)
(-14)*(180)
(-15)*(168)
(-18)*(140)
(-20)*(126)
(-21)*(120)
(-24)*(105)
(-28)*(90)
(-30)*(84)
(-35)*(72)
(-36)*(70)
(-40)*(63)
(-42)*(60)
(-45)*(56)

note: remember, the product of a negative and a positive number is a negative number


Now which of these pairs add to -23? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -23

First NumberSecond NumberSum
1-25201+(-2520)=-2519
2-12602+(-1260)=-1258
3-8403+(-840)=-837
4-6304+(-630)=-626
5-5045+(-504)=-499
6-4206+(-420)=-414
7-3607+(-360)=-353
8-3158+(-315)=-307
9-2809+(-280)=-271
10-25210+(-252)=-242
12-21012+(-210)=-198
14-18014+(-180)=-166
15-16815+(-168)=-153
18-14018+(-140)=-122
20-12620+(-126)=-106
21-12021+(-120)=-99
24-10524+(-105)=-81
28-9028+(-90)=-62
30-8430+(-84)=-54
35-7235+(-72)=-37
36-7036+(-70)=-34
40-6340+(-63)=-23
42-6042+(-60)=-18
45-5645+(-56)=-11
-12520-1+2520=2519
-21260-2+1260=1258
-3840-3+840=837
-4630-4+630=626
-5504-5+504=499
-6420-6+420=414
-7360-7+360=353
-8315-8+315=307
-9280-9+280=271
-10252-10+252=242
-12210-12+210=198
-14180-14+180=166
-15168-15+168=153
-18140-18+140=122
-20126-20+126=106
-21120-21+120=99
-24105-24+105=81
-2890-28+90=62
-3084-30+84=54
-3572-35+72=37
-3670-36+70=34
-4063-40+63=23
-4260-42+60=18
-4556-45+56=11



From this list we can see that 40 and -63 add up to -23 and multiply to -2520


Now looking at the expression , replace with (notice adds up to . So it is equivalent to )




Now let's factor by grouping:


Group like terms


Factor out the GCF of out of the first group. Factor out the GCF of out of the second group


Since we have a common term of , we can combine like terms

So factors to


So this also means that factors to (since is equivalent to )



------------------------------------------------------------



Answer:
So factors to


So one of the factors of is D)
RELATED QUESTIONS

when 35z^2-23z-72 is factored completely, one of the factors is: (answered by scott8148)
Divide the following expression: 27z+23z^2+6z^3 / 2z+3 A) 3z^2+7z+3 and a remainder of... (answered by stanbon)
divide the following expression 27z+23z^2+6z^3/2z+3 a. 3z^2+7z+3 and a remainder or... (answered by ewatrrr)
when z^2+5z-84 is factored completely, one of the factors... (answered by jim_thompson5910)
The Question Is: Find the third-degree polynomial with real coefficients and with zeros... (answered by venugopalramana)
(3z^2 + 7z + 9) + (6z^2 + 3z -3) - ( -5z^2... (answered by bonster)
A pentagon has 1 side of legth zcm, 2 sides of length (z+2)cm each, 1 side of length 5z... (answered by shree840)
answer for... (answered by stanbon)
Simplify the expression : 7w - 7z... (answered by stanbon)