Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(5m2 - 36m) + 64
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 5m2-36m+64
The first term is, 5m2 its coefficient is 5 .
The middle term is, -36m its coefficient is -36 .
The last term, "the constant", is +64
Step-1 : Multiply the coefficient of the first term by the constant 5 • 64 = 320
Step-2 : Find two factors of 320 whose sum equals the coefficient of the middle term, which is -36 .
| -320 | + | -1 | = | -321 | ||
| -160 | + | -2 | = | -162 | ||
| -80 | + | -4 | = | -84 | ||
| -64 | + | -5 | = | -69 | ||
| -40 | + | -8 | = | -48 | ||
| -32 | + | -10 | = | -42 | ||
| -20 | + | -16 | = | -36 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -20 and -16
5m2 - 20m - 16m - 64
Step-4 : Add up the first 2 terms, pulling out like factors :
5m • (m-4)
Add up the last 2 terms, pulling out common factors :
16 • (m-4)
Step-5 : Add up the four terms of step 4 :
(5m-16) • (m-4)
Which is the desired factorization
Final result :
(m - 4) • (5m - 16)
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