SOLUTION: I just help doing some step by step problems can someone show me how to do -30x(squared)+15x + 90 step by step please and 8x(squared)+10x -3 thanks for any help
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Question 200463: I just help doing some step by step problems can someone show me how to do -30x(squared)+15x + 90 step by step please and 8x(squared)+10x -3 thanks for any help
Found 2 solutions by jim_thompson5910, Earlsdon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'm assuming that you want to factor these expressions.
# 1
Start with the given expression
Factor out the GCF
Now let's focus on the inner expression
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Looking at we can see that the first term is and the last term is where the coefficients are 2 and -6 respectively.
Now multiply the first coefficient 2 and the last coefficient -6 to get -12. Now what two numbers multiply to -12 and add to the middle coefficient -1? Let's list all of the factors of -12:
Factors of -12:
1,2,3,4,6,12
-1,-2,-3,-4,-6,-12 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -12
(1)*(-12)
(2)*(-6)
(3)*(-4)
(-1)*(12)
(-2)*(6)
(-3)*(4)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to -1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -1
| First Number | Second Number | Sum | | 1 | -12 | 1+(-12)=-11 |
| 2 | -6 | 2+(-6)=-4 |
| 3 | -4 | 3+(-4)=-1 |
| -1 | 12 | -1+12=11 |
| -2 | 6 | -2+6=4 |
| -3 | 4 | -3+4=1 |
From this list we can see that 3 and -4 add up to -1 and multiply to -12
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 )
------------------------------------------------------------
So our expression goes from and factors further to
------------------
Answer:
So completely factors to
# 2
Looking at we can see that the first term is and the last term is where the coefficients are 8 and -3 respectively.
Now multiply the first coefficient 8 and the last coefficient -3 to get -24. Now what two numbers multiply to -24 and add to the middle coefficient 10? Let's list all of the factors of -24:
Factors of -24:
1,2,3,4,6,8,12,24
-1,-2,-3,-4,-6,-8,-12,-24 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -24
(1)*(-24)
(2)*(-12)
(3)*(-8)
(4)*(-6)
(-1)*(24)
(-2)*(12)
(-3)*(8)
(-4)*(6)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to 10? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 10
| First Number | Second Number | Sum | | 1 | -24 | 1+(-24)=-23 |
| 2 | -12 | 2+(-12)=-10 |
| 3 | -8 | 3+(-8)=-5 |
| 4 | -6 | 4+(-6)=-2 |
| -1 | 24 | -1+24=23 |
| -2 | 12 | -2+12=10 |
| -3 | 8 | -3+8=5 |
| -4 | 6 | -4+6=2 |
From this list we can see that -2 and 12 add up to 10 and multiply to -24
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
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
While you don't say, I suspect that you want to factor these expressions, right?
Factor:
First, factor out a -15 because that's a factor of each of the three terms in the expression.
Notice the sign change in the terms! Now factor the trinomial.
Factor:
Factor the trinomial.
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