Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((2•3x2) + 13x) - 63
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 6x2+13x-63
The first term is, 6x2 its coefficient is 6 .
The middle term is, +13x its coefficient is 13 .
The last term, "the constant", is -63
Step-1 : Multiply the coefficient of the first term by the constant 6 • -63 = -378
Step-2 : Find two factors of -378 whose sum equals the coefficient of the middle term, which is 13 .
| -378 | + | 1 | = | -377 | ||
| -189 | + | 2 | = | -187 | ||
| -126 | + | 3 | = | -123 | ||
| -63 | + | 6 | = | -57 | ||
| -54 | + | 7 | = | -47 | ||
| -42 | + | 9 | = | -33 | ||
| -27 | + | 14 | = | -13 | ||
| -21 | + | 18 | = | -3 | ||
| -18 | + | 21 | = | 3 | ||
| -14 | + | 27 | = | 13 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -14 and 27
6x2 - 14x + 27x - 63
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (3x-7)
Add up the last 2 terms, pulling out common factors :
9 • (3x-7)
Step-5 : Add up the four terms of step 4 :
(2x+9) • (3x-7)
Which is the desired factorization
Final result :
(3x - 7) • (2x + 9)
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