Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((2•5x2) + 21x) - 10
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 10x2+21x-10
The first term is, 10x2 its coefficient is 10 .
The middle term is, +21x its coefficient is 21 .
The last term, "the constant", is -10
Step-1 : Multiply the coefficient of the first term by the constant 10 • -10 = -100
Step-2 : Find two factors of -100 whose sum equals the coefficient of the middle term, which is 21 .
| -100 | + | 1 | = | -99 | ||
| -50 | + | 2 | = | -48 | ||
| -25 | + | 4 | = | -21 | ||
| -20 | + | 5 | = | -15 | ||
| -10 | + | 10 | = | 0 | ||
| -5 | + | 20 | = | 15 | ||
| -4 | + | 25 | = | 21 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 25
10x2 - 4x + 25x - 10
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (5x-2)
Add up the last 2 terms, pulling out common factors :
5 • (5x-2)
Step-5 : Add up the four terms of step 4 :
(2x+5) • (5x-2)
Which is the desired factorization
Final result :
(5x - 2) • (2x + 5)
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