Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((32•5x2) - 73x) + 14
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 45x2-73x+14
The first term is, 45x2 its coefficient is 45 .
The middle term is, -73x its coefficient is -73 .
The last term, "the constant", is +14
Step-1 : Multiply the coefficient of the first term by the constant 45 • 14 = 630
Step-2 : Find two factors of 630 whose sum equals the coefficient of the middle term, which is -73 .
| -630 | + | -1 | = | -631 | ||
| -315 | + | -2 | = | -317 | ||
| -210 | + | -3 | = | -213 | ||
| -126 | + | -5 | = | -131 | ||
| -105 | + | -6 | = | -111 | ||
| -90 | + | -7 | = | -97 | ||
| -70 | + | -9 | = | -79 | ||
| -63 | + | -10 | = | -73 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -63 and -10
45x2 - 63x - 10x - 14
Step-4 : Add up the first 2 terms, pulling out like factors :
9x • (5x-7)
Add up the last 2 terms, pulling out common factors :
2 • (5x-7)
Step-5 : Add up the four terms of step 4 :
(9x-2) • (5x-7)
Which is the desired factorization
Final result :
(5x - 7) • (9x - 2)
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