Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(2x2 + 17x) + 21
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 2x2+17x+21
The first term is, 2x2 its coefficient is 2 .
The middle term is, +17x its coefficient is 17 .
The last term, "the constant", is +21
Step-1 : Multiply the coefficient of the first term by the constant 2 • 21 = 42
Step-2 : Find two factors of 42 whose sum equals the coefficient of the middle term, which is 17 .
| -42 | + | -1 | = | -43 | ||
| -21 | + | -2 | = | -23 | ||
| -14 | + | -3 | = | -17 | ||
| -7 | + | -6 | = | -13 | ||
| -6 | + | -7 | = | -13 | ||
| -3 | + | -14 | = | -17 | ||
| -2 | + | -21 | = | -23 | ||
| -1 | + | -42 | = | -43 | ||
| 1 | + | 42 | = | 43 | ||
| 2 | + | 21 | = | 23 | ||
| 3 | + | 14 | = | 17 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 3 and 14
2x2 + 3x + 14x + 21
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (2x+3)
Add up the last 2 terms, pulling out common factors :
7 • (2x+3)
Step-5 : Add up the four terms of step 4 :
(x+7) • (2x+3)
Which is the desired factorization
Final result :
(2x + 3) • (x + 7)
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