Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(3x2 + 25x) + 28
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 3x2+25x+28
The first term is, 3x2 its coefficient is 3 .
The middle term is, +25x its coefficient is 25 .
The last term, "the constant", is +28
Step-1 : Multiply the coefficient of the first term by the constant 3 • 28 = 84
Step-2 : Find two factors of 84 whose sum equals the coefficient of the middle term, which is 25 .
| -84 | + | -1 | = | -85 | ||
| -42 | + | -2 | = | -44 | ||
| -28 | + | -3 | = | -31 | ||
| -21 | + | -4 | = | -25 | ||
| -14 | + | -6 | = | -20 | ||
| -12 | + | -7 | = | -19 | ||
| -7 | + | -12 | = | -19 | ||
| -6 | + | -14 | = | -20 | ||
| -4 | + | -21 | = | -25 | ||
| -3 | + | -28 | = | -31 | ||
| -2 | + | -42 | = | -44 | ||
| -1 | + | -84 | = | -85 | ||
| 1 | + | 84 | = | 85 | ||
| 2 | + | 42 | = | 44 | ||
| 3 | + | 28 | = | 31 | ||
| 4 | + | 21 | = | 25 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 4 and 21
3x2 + 4x + 21x + 28
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (3x+4)
Add up the last 2 terms, pulling out common factors :
7 • (3x+4)
Step-5 : Add up the four terms of step 4 :
(x+7) • (3x+4)
Which is the desired factorization
Final result :
(3x + 4) • (x + 7)
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