Solution - Simplification or other simple results
Step by Step Solution
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
Step 1 :
Equation at the end of step 1 :
((5•7x2) - 2x) - 48
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 35x2-2x-48
The first term is, 35x2 its coefficient is 35 .
The middle term is, -2x its coefficient is -2 .
The last term, "the constant", is -48
Step-1 : Multiply the coefficient of the first term by the constant 35 • -48 = -1680
Step-2 : Find two factors of -1680 whose sum equals the coefficient of the middle term, which is -2 .
| -1680 | + | 1 | = | -1679 | ||
| -840 | + | 2 | = | -838 | ||
| -560 | + | 3 | = | -557 | ||
| -420 | + | 4 | = | -416 | ||
| -336 | + | 5 | = | -331 | ||
| -280 | + | 6 | = | -274 | ||
| -240 | + | 7 | = | -233 | ||
| -210 | + | 8 | = | -202 | ||
| -168 | + | 10 | = | -158 | ||
| -140 | + | 12 | = | -128 | ||
| -120 | + | 14 | = | -106 | ||
| -112 | + | 15 | = | -97 | ||
| -105 | + | 16 | = | -89 | ||
| -84 | + | 20 | = | -64 | ||
| -80 | + | 21 | = | -59 | ||
| -70 | + | 24 | = | -46 | ||
| -60 | + | 28 | = | -32 | ||
| -56 | + | 30 | = | -26 | ||
| -48 | + | 35 | = | -13 | ||
| -42 | + | 40 | = | -2 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -42 and 40
35x2 - 42x + 40x - 48
Step-4 : Add up the first 2 terms, pulling out like factors :
7x • (5x-6)
Add up the last 2 terms, pulling out common factors :
8 • (5x-6)
Step-5 : Add up the four terms of step 4 :
(7x+8) • (5x-6)
Which is the desired factorization
Final result :
(5x - 6) • (7x + 8)
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