Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((3•5z2) - 8z) - 16
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 15z2-8z-16
The first term is, 15z2 its coefficient is 15 .
The middle term is, -8z its coefficient is -8 .
The last term, "the constant", is -16
Step-1 : Multiply the coefficient of the first term by the constant 15 • -16 = -240
Step-2 : Find two factors of -240 whose sum equals the coefficient of the middle term, which is -8 .
| -240 | + | 1 | = | -239 | ||
| -120 | + | 2 | = | -118 | ||
| -80 | + | 3 | = | -77 | ||
| -60 | + | 4 | = | -56 | ||
| -48 | + | 5 | = | -43 | ||
| -40 | + | 6 | = | -34 | ||
| -30 | + | 8 | = | -22 | ||
| -24 | + | 10 | = | -14 | ||
| -20 | + | 12 | = | -8 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -20 and 12
15z2 - 20z + 12z - 16
Step-4 : Add up the first 2 terms, pulling out like factors :
5z • (3z-4)
Add up the last 2 terms, pulling out common factors :
4 • (3z-4)
Step-5 : Add up the four terms of step 4 :
(5z+4) • (3z-4)
Which is the desired factorization
Final result :
(3z - 4) • (5z + 4)
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