Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring x2+5x-84
The first term is, x2 its coefficient is 1 .
The middle term is, +5x its coefficient is 5 .
The last term, "the constant", is -84
Step-1 : Multiply the coefficient of the first term by the constant 1 • -84 = -84
Step-2 : Find two factors of -84 whose sum equals the coefficient of the middle term, which is 5 .
| -84 | + | 1 | = | -83 | ||
| -42 | + | 2 | = | -40 | ||
| -28 | + | 3 | = | -25 | ||
| -21 | + | 4 | = | -17 | ||
| -14 | + | 6 | = | -8 | ||
| -12 | + | 7 | = | -5 | ||
| -7 | + | 12 | = | 5 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and 12
x2 - 7x + 12x - 84
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-7)
Add up the last 2 terms, pulling out common factors :
12 • (x-7)
Step-5 : Add up the four terms of step 4 :
(x+12) • (x-7)
Which is the desired factorization
Final result :
(x + 12) • (x - 7)
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