Solution - Simplification or other simple results
Step by Step Solution
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "a2" was replaced by "a^2".
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring a2+17a+72
The first term is, a2 its coefficient is 1 .
The middle term is, +17a its coefficient is 17 .
The last term, "the constant", is +72
Step-1 : Multiply the coefficient of the first term by the constant 1 • 72 = 72
Step-2 : Find two factors of 72 whose sum equals the coefficient of the middle term, which is 17 .
| -72 | + | -1 | = | -73 | ||
| -36 | + | -2 | = | -38 | ||
| -24 | + | -3 | = | -27 | ||
| -18 | + | -4 | = | -22 | ||
| -12 | + | -6 | = | -18 | ||
| -9 | + | -8 | = | -17 | ||
| -8 | + | -9 | = | -17 | ||
| -6 | + | -12 | = | -18 | ||
| -4 | + | -18 | = | -22 | ||
| -3 | + | -24 | = | -27 | ||
| -2 | + | -36 | = | -38 | ||
| -1 | + | -72 | = | -73 | ||
| 1 | + | 72 | = | 73 | ||
| 2 | + | 36 | = | 38 | ||
| 3 | + | 24 | = | 27 | ||
| 4 | + | 18 | = | 22 | ||
| 6 | + | 12 | = | 18 | ||
| 8 | + | 9 | = | 17 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 8 and 9
a2 + 8a + 9a + 72
Step-4 : Add up the first 2 terms, pulling out like factors :
a • (a+8)
Add up the last 2 terms, pulling out common factors :
9 • (a+8)
Step-5 : Add up the four terms of step 4 :
(a+9) • (a+8)
Which is the desired factorization
Final result :
(a + 9) • (a + 8)
How did we do?
Please leave us feedback.