Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(2x2 + 15x) + 25
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 2x2+15x+25
The first term is, 2x2 its coefficient is 2 .
The middle term is, +15x its coefficient is 15 .
The last term, "the constant", is +25
Step-1 : Multiply the coefficient of the first term by the constant 2 • 25 = 50
Step-2 : Find two factors of 50 whose sum equals the coefficient of the middle term, which is 15 .
| -50 | + | -1 | = | -51 | ||
| -25 | + | -2 | = | -27 | ||
| -10 | + | -5 | = | -15 | ||
| -5 | + | -10 | = | -15 | ||
| -2 | + | -25 | = | -27 | ||
| -1 | + | -50 | = | -51 | ||
| 1 | + | 50 | = | 51 | ||
| 2 | + | 25 | = | 27 | ||
| 5 | + | 10 | = | 15 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 5 and 10
2x2 + 5x + 10x + 25
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (2x+5)
Add up the last 2 terms, pulling out common factors :
5 • (2x+5)
Step-5 : Add up the four terms of step 4 :
(x+5) • (2x+5)
Which is the desired factorization
Final result :
(2x + 5) • (x + 5)
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