Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((3•5x2) + 31x) + 10
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 15x2+31x+10
The first term is, 15x2 its coefficient is 15 .
The middle term is, +31x its coefficient is 31 .
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 31 .
| -150 | + | -1 | = | -151 | ||
| -75 | + | -2 | = | -77 | ||
| -50 | + | -3 | = | -53 | ||
| -30 | + | -5 | = | -35 | ||
| -25 | + | -6 | = | -31 | ||
| -15 | + | -10 | = | -25 | ||
| -10 | + | -15 | = | -25 | ||
| -6 | + | -25 | = | -31 | ||
| -5 | + | -30 | = | -35 | ||
| -3 | + | -50 | = | -53 | ||
| -2 | + | -75 | = | -77 | ||
| -1 | + | -150 | = | -151 | ||
| 1 | + | 150 | = | 151 | ||
| 2 | + | 75 | = | 77 | ||
| 3 | + | 50 | = | 53 | ||
| 5 | + | 30 | = | 35 | ||
| 6 | + | 25 | = | 31 | 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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