Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((-12x + (2•5x2)) + 30x) - 36
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
10x2 + 18x - 36 = 2 • (5x2 + 9x - 18)
Trying to factor by splitting the middle term
3.2 Factoring 5x2 + 9x - 18
The first term is, 5x2 its coefficient is 5 .
The middle term is, +9x its coefficient is 9 .
The last term, "the constant", is -18
Step-1 : Multiply the coefficient of the first term by the constant 5 • -18 = -90
Step-2 : Find two factors of -90 whose sum equals the coefficient of the middle term, which is 9 .
| -90 | + | 1 | = | -89 | ||
| -45 | + | 2 | = | -43 | ||
| -30 | + | 3 | = | -27 | ||
| -18 | + | 5 | = | -13 | ||
| -15 | + | 6 | = | -9 | ||
| -10 | + | 9 | = | -1 | ||
| -9 | + | 10 | = | 1 | ||
| -6 | + | 15 | = | 9 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 15
5x2 - 6x + 15x - 18
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (5x-6)
Add up the last 2 terms, pulling out common factors :
3 • (5x-6)
Step-5 : Add up the four terms of step 4 :
(x+3) • (5x-6)
Which is the desired factorization
Final result :
2 • (5x - 6) • (x + 3)
How did we do?
Please leave us feedback.