SOLUTION: Rewrite the middle term as the sum of two terms and then factor completely.
4z squared -18z squared -10z
Algebra.Com
Question 115207This question is from textbook Beginning Algebra
: Rewrite the middle term as the sum of two terms and then factor completely.
4z squared -18z squared -10z
This question is from textbook Beginning Algebra
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 4 and -10 respectively.
Now multiply the first coefficient 4 and the last coefficient -10 to get -40. Now what two numbers multiply to -40 and add to the middle coefficient -18? Let's list all of the factors of -40:
Factors of -40:
1,2,4,5,8,10,20,40
-1,-2,-4,-5,-8,-10,-20,-40 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -40
(1)*(-40)
(2)*(-20)
(4)*(-10)
(5)*(-8)
(-1)*(40)
(-2)*(20)
(-4)*(10)
(-5)*(8)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to -18? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -18
| First Number | Second Number | Sum | | 1 | -40 | 1+(-40)=-39 |
| 2 | -20 | 2+(-20)=-18 |
| 4 | -10 | 4+(-10)=-6 |
| 5 | -8 | 5+(-8)=-3 |
| -1 | 40 | -1+40=39 |
| -2 | 20 | -2+20=18 |
| -4 | 10 | -4+10=6 |
| -5 | 8 | -5+8=3 |
From this list we can see that 2 and -20 add up to -18 and multiply to -40
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
RELATED QUESTIONS
Rewrite the middle term as the sum of two terms and then factor completely.
4z^3 -... (answered by Fermat)
Rewrite the middle term as the sum of two terms and then factor completely
4z^3 -... (answered by stanbon)
Rewrite the middle term as the sum of two terms and then factor completely.
4z^3 -... (answered by funmath)
Rewrite the middle term as the sum of two terms and then factor completely
4z³ -18z² - (answered by stanbon)
rewrite the middle term as the sum of two terms and then factor completly... (answered by checkley75)
I don't understand how to do this...
REWRITE THE MIDDLE TERM AS THE SUM OF TWO TERMS... (answered by psbhowmick)
Rewrite the middle term as the sum of two terms and then factor completely.... (answered by jgr45)
can some one check this for me please?I have to rewrite the middle term as the sum of two (answered by checkley75)
I do not know what this is asking me. Please help.
Rewrite the middle term as the sum of (answered by checkley75)