Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((2•3c2) + 41c) + 63
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 6c2+41c+63
The first term is, 6c2 its coefficient is 6 .
The middle term is, +41c its coefficient is 41 .
The last term, "the constant", is +63
Step-1 : Multiply the coefficient of the first term by the constant 6 • 63 = 378
Step-2 : Find two factors of 378 whose sum equals the coefficient of the middle term, which is 41 .
| -378 | + | -1 | = | -379 | ||
| -189 | + | -2 | = | -191 | ||
| -126 | + | -3 | = | -129 | ||
| -63 | + | -6 | = | -69 | ||
| -54 | + | -7 | = | -61 | ||
| -42 | + | -9 | = | -51 | ||
| -27 | + | -14 | = | -41 | ||
| -21 | + | -18 | = | -39 | ||
| -18 | + | -21 | = | -39 | ||
| -14 | + | -27 | = | -41 | ||
| -9 | + | -42 | = | -51 | ||
| -7 | + | -54 | = | -61 | ||
| -6 | + | -63 | = | -69 | ||
| -3 | + | -126 | = | -129 | ||
| -2 | + | -189 | = | -191 | ||
| -1 | + | -378 | = | -379 | ||
| 1 | + | 378 | = | 379 | ||
| 2 | + | 189 | = | 191 | ||
| 3 | + | 126 | = | 129 | ||
| 6 | + | 63 | = | 69 | ||
| 7 | + | 54 | = | 61 | ||
| 9 | + | 42 | = | 51 | ||
| 14 | + | 27 | = | 41 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 14 and 27
6c2 + 14c + 27c + 63
Step-4 : Add up the first 2 terms, pulling out like factors :
2c • (3c+7)
Add up the last 2 terms, pulling out common factors :
9 • (3c+7)
Step-5 : Add up the four terms of step 4 :
(2c+9) • (3c+7)
Which is the desired factorization
Final result :
(3c + 7) • (2c + 9)
How did we do?
Please leave us feedback.