Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((2•3•5x2) + 13x) - 10
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 30x2+13x-10
The first term is, 30x2 its coefficient is 30 .
The middle term is, +13x its coefficient is 13 .
The last term, "the constant", is -10
Step-1 : Multiply the coefficient of the first term by the constant 30 • -10 = -300
Step-2 : Find two factors of -300 whose sum equals the coefficient of the middle term, which is 13 .
| -300 | + | 1 | = | -299 | ||
| -150 | + | 2 | = | -148 | ||
| -100 | + | 3 | = | -97 | ||
| -75 | + | 4 | = | -71 | ||
| -60 | + | 5 | = | -55 | ||
| -50 | + | 6 | = | -44 | ||
| -30 | + | 10 | = | -20 | ||
| -25 | + | 12 | = | -13 | ||
| -20 | + | 15 | = | -5 | ||
| -15 | + | 20 | = | 5 | ||
| -12 | + | 25 | = | 13 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and 25
30x2 - 12x + 25x - 10
Step-4 : Add up the first 2 terms, pulling out like factors :
6x • (5x-2)
Add up the last 2 terms, pulling out common factors :
5 • (5x-2)
Step-5 : Add up the four terms of step 4 :
(6x+5) • (5x-2)
Which is the desired factorization
Final result :
(5x - 2) • (6x + 5)
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