Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((2•5x2) + 33x) + 20
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 10x2+33x+20
The first term is, 10x2 its coefficient is 10 .
The middle term is, +33x its coefficient is 33 .
The last term, "the constant", is +20
Step-1 : Multiply the coefficient of the first term by the constant 10 • 20 = 200
Step-2 : Find two factors of 200 whose sum equals the coefficient of the middle term, which is 33 .
| -200 | + | -1 | = | -201 | ||
| -100 | + | -2 | = | -102 | ||
| -50 | + | -4 | = | -54 | ||
| -40 | + | -5 | = | -45 | ||
| -25 | + | -8 | = | -33 | ||
| -20 | + | -10 | = | -30 | ||
| -10 | + | -20 | = | -30 | ||
| -8 | + | -25 | = | -33 | ||
| -5 | + | -40 | = | -45 | ||
| -4 | + | -50 | = | -54 | ||
| -2 | + | -100 | = | -102 | ||
| -1 | + | -200 | = | -201 | ||
| 1 | + | 200 | = | 201 | ||
| 2 | + | 100 | = | 102 | ||
| 4 | + | 50 | = | 54 | ||
| 5 | + | 40 | = | 45 | ||
| 8 | + | 25 | = | 33 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 8 and 25
10x2 + 8x + 25x + 20
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (5x+4)
Add up the last 2 terms, pulling out common factors :
5 • (5x+4)
Step-5 : Add up the four terms of step 4 :
(2x+5) • (5x+4)
Which is the desired factorization
Final result :
(5x + 4) • (2x + 5)
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