Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(22x2 + 19x) + 12
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 4x2+19x+12
The first term is, 4x2 its coefficient is 4 .
The middle term is, +19x its coefficient is 19 .
The last term, "the constant", is +12
Step-1 : Multiply the coefficient of the first term by the constant 4 • 12 = 48
Step-2 : Find two factors of 48 whose sum equals the coefficient of the middle term, which is 19 .
| -48 | + | -1 | = | -49 | ||
| -24 | + | -2 | = | -26 | ||
| -16 | + | -3 | = | -19 | ||
| -12 | + | -4 | = | -16 | ||
| -8 | + | -6 | = | -14 | ||
| -6 | + | -8 | = | -14 | ||
| -4 | + | -12 | = | -16 | ||
| -3 | + | -16 | = | -19 | ||
| -2 | + | -24 | = | -26 | ||
| -1 | + | -48 | = | -49 | ||
| 1 | + | 48 | = | 49 | ||
| 2 | + | 24 | = | 26 | ||
| 3 | + | 16 | = | 19 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 3 and 16
4x2 + 3x + 16x + 12
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (4x+3)
Add up the last 2 terms, pulling out common factors :
4 • (4x+3)
Step-5 : Add up the four terms of step 4 :
(x+4) • (4x+3)
Which is the desired factorization
Final result :
(4x + 3) • (x + 4)
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