Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((0 - 24t2) + 24t) + 7
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring -16t2+24t+7
The first term is, -16t2 its coefficient is -16 .
The middle term is, +24t its coefficient is 24 .
The last term, "the constant", is +7
Step-1 : Multiply the coefficient of the first term by the constant -16 • 7 = -112
Step-2 : Find two factors of -112 whose sum equals the coefficient of the middle term, which is 24 .
| -112 | + | 1 | = | -111 | ||
| -56 | + | 2 | = | -54 | ||
| -28 | + | 4 | = | -24 | ||
| -16 | + | 7 | = | -9 | ||
| -14 | + | 8 | = | -6 | ||
| -8 | + | 14 | = | 6 | ||
| -7 | + | 16 | = | 9 | ||
| -4 | + | 28 | = | 24 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 28
-16t2 - 4t + 28t + 7
Step-4 : Add up the first 2 terms, pulling out like factors :
-4t • (4t+1)
Add up the last 2 terms, pulling out common factors :
7 • (4t+1)
Step-5 : Add up the four terms of step 4 :
(-4t+7) • (4t+1)
Which is the desired factorization
Final result :
(4t + 1) • (7 - 4t)
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