Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(22x2 + 19x) + 21
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 4x2+19x+21
The first term is, 4x2 its coefficient is 4 .
The middle term is, +19x its coefficient is 19 .
The last term, "the constant", is +21
Step-1 : Multiply the coefficient of the first term by the constant 4 • 21 = 84
Step-2 : Find two factors of 84 whose sum equals the coefficient of the middle term, which is 19 .
| -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 | ||
| 6 | + | 14 | = | 20 | ||
| 7 | + | 12 | = | 19 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 7 and 12
4x2 + 7x + 12x + 21
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (4x+7)
Add up the last 2 terms, pulling out common factors :
3 • (4x+7)
Step-5 : Add up the four terms of step 4 :
(x+3) • (4x+7)
Which is the desired factorization
Final result :
(4x + 7) • (x + 3)
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