Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((3•5x2) + 19x) - 10
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 15x2+19x-10
The first term is, 15x2 its coefficient is 15 .
The middle term is, +19x its coefficient is 19 .
The last term, "the constant", is -10
Step-1 : Multiply the coefficient of the first term by the constant 15 • -10 = -150
Step-2 : Find two factors of -150 whose sum equals the coefficient of the middle term, which is 19 .
| -150 | + | 1 | = | -149 | ||
| -75 | + | 2 | = | -73 | ||
| -50 | + | 3 | = | -47 | ||
| -30 | + | 5 | = | -25 | ||
| -25 | + | 6 | = | -19 | ||
| -15 | + | 10 | = | -5 | ||
| -10 | + | 15 | = | 5 | ||
| -6 | + | 25 | = | 19 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 25
15x2 - 6x + 25x - 10
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (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 :
(3x+5) • (5x-2)
Which is the desired factorization
Final result :
(5x - 2) • (3x + 5)
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