Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(3x2 + 14x) + 15
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 3x2+14x+15
The first term is, 3x2 its coefficient is 3 .
The middle term is, +14x its coefficient is 14 .
The last term, "the constant", is +15
Step-1 : Multiply the coefficient of the first term by the constant 3 • 15 = 45
Step-2 : Find two factors of 45 whose sum equals the coefficient of the middle term, which is 14 .
| -45 | + | -1 | = | -46 | ||
| -15 | + | -3 | = | -18 | ||
| -9 | + | -5 | = | -14 | ||
| -5 | + | -9 | = | -14 | ||
| -3 | + | -15 | = | -18 | ||
| -1 | + | -45 | = | -46 | ||
| 1 | + | 45 | = | 46 | ||
| 3 | + | 15 | = | 18 | ||
| 5 | + | 9 | = | 14 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 5 and 9
3x2 + 5x + 9x + 15
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (3x+5)
Add up the last 2 terms, pulling out common factors :
3 • (3x+5)
Step-5 : Add up the four terms of step 4 :
(x+3) • (3x+5)
Which is the desired factorization
Final result :
(3x + 5) • (x + 3)
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