Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring m2+15m+54
The first term is, m2 its coefficient is 1 .
The middle term is, +15m its coefficient is 15 .
The last term, "the constant", is +54
Step-1 : Multiply the coefficient of the first term by the constant 1 • 54 = 54
Step-2 : Find two factors of 54 whose sum equals the coefficient of the middle term, which is 15 .
| -54 | + | -1 | = | -55 | ||
| -27 | + | -2 | = | -29 | ||
| -18 | + | -3 | = | -21 | ||
| -9 | + | -6 | = | -15 | ||
| -6 | + | -9 | = | -15 | ||
| -3 | + | -18 | = | -21 | ||
| -2 | + | -27 | = | -29 | ||
| -1 | + | -54 | = | -55 | ||
| 1 | + | 54 | = | 55 | ||
| 2 | + | 27 | = | 29 | ||
| 3 | + | 18 | = | 21 | ||
| 6 | + | 9 | = | 15 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 6 and 9
m2 + 6m + 9m + 54
Step-4 : Add up the first 2 terms, pulling out like factors :
m • (m+6)
Add up the last 2 terms, pulling out common factors :
9 • (m+6)
Step-5 : Add up the four terms of step 4 :
(m+9) • (m+6)
Which is the desired factorization
Final result :
(m + 9) • (m + 6)
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