Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((3•5x2) + 52x) + 45
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 15x2+52x+45
The first term is, 15x2 its coefficient is 15 .
The middle term is, +52x its coefficient is 52 .
The last term, "the constant", is +45
Step-1 : Multiply the coefficient of the first term by the constant 15 • 45 = 675
Step-2 : Find two factors of 675 whose sum equals the coefficient of the middle term, which is 52 .
| -675 | + | -1 | = | -676 | ||
| -225 | + | -3 | = | -228 | ||
| -135 | + | -5 | = | -140 | ||
| -75 | + | -9 | = | -84 | ||
| -45 | + | -15 | = | -60 | ||
| -27 | + | -25 | = | -52 | ||
| -25 | + | -27 | = | -52 | ||
| -15 | + | -45 | = | -60 | ||
| -9 | + | -75 | = | -84 | ||
| -5 | + | -135 | = | -140 | ||
| -3 | + | -225 | = | -228 | ||
| -1 | + | -675 | = | -676 | ||
| 1 | + | 675 | = | 676 | ||
| 3 | + | 225 | = | 228 | ||
| 5 | + | 135 | = | 140 | ||
| 9 | + | 75 | = | 84 | ||
| 15 | + | 45 | = | 60 | ||
| 25 | + | 27 | = | 52 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 25 and 27
15x2 + 25x + 27x + 45
Step-4 : Add up the first 2 terms, pulling out like factors :
5x • (3x+5)
Add up the last 2 terms, pulling out common factors :
9 • (3x+5)
Step-5 : Add up the four terms of step 4 :
(5x+9) • (3x+5)
Which is the desired factorization
Final result :
(3x + 5) • (5x + 9)
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