Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(5x2 + 22x) + 21
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 5x2+22x+21
The first term is, 5x2 its coefficient is 5 .
The middle term is, +22x its coefficient is 22 .
The last term, "the constant", is +21
Step-1 : Multiply the coefficient of the first term by the constant 5 • 21 = 105
Step-2 : Find two factors of 105 whose sum equals the coefficient of the middle term, which is 22 .
| -105 | + | -1 | = | -106 | ||
| -35 | + | -3 | = | -38 | ||
| -21 | + | -5 | = | -26 | ||
| -15 | + | -7 | = | -22 | ||
| -7 | + | -15 | = | -22 | ||
| -5 | + | -21 | = | -26 | ||
| -3 | + | -35 | = | -38 | ||
| -1 | + | -105 | = | -106 | ||
| 1 | + | 105 | = | 106 | ||
| 3 | + | 35 | = | 38 | ||
| 5 | + | 21 | = | 26 | ||
| 7 | + | 15 | = | 22 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 7 and 15
5x2 + 7x + 15x + 21
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (5x+7)
Add up the last 2 terms, pulling out common factors :
3 • (5x+7)
Step-5 : Add up the four terms of step 4 :
(x+3) • (5x+7)
Which is the desired factorization
Final result :
(5x + 7) • (x + 3)
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