Solution - Simplification or other simple results
Other Ways to Solve:
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((2•3•5x2) - 35x) - 100
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
30x2 - 35x - 100 = 5 • (6x2 - 7x - 20)
Trying to factor by splitting the middle term
3.2 Factoring 6x2 - 7x - 20
The first term is, 6x2 its coefficient is 6 .
The middle term is, -7x its coefficient is -7 .
The last term, "the constant", is -20
Step-1 : Multiply the coefficient of the first term by the constant 6 • -20 = -120
Step-2 : Find two factors of -120 whose sum equals the coefficient of the middle term, which is -7 .
-120 | + | 1 | = | -119 | ||
-60 | + | 2 | = | -58 | ||
-40 | + | 3 | = | -37 | ||
-30 | + | 4 | = | -26 | ||
-24 | + | 5 | = | -19 | ||
-20 | + | 6 | = | -14 | ||
-15 | + | 8 | = | -7 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and 8
6x2 - 15x + 8x - 20
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (2x-5)
Add up the last 2 terms, pulling out common factors :
4 • (2x-5)
Step-5 : Add up the four terms of step 4 :
(3x+4) • (2x-5)
Which is the desired factorization
Final result :
5 • (2x - 5) • (3x + 4)
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