Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(23x2 + 10x) + 3
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 8x2+10x+3
The first term is, 8x2 its coefficient is 8 .
The middle term is, +10x its coefficient is 10 .
The last term, "the constant", is +3
Step-1 : Multiply the coefficient of the first term by the constant 8 • 3 = 24
Step-2 : Find two factors of 24 whose sum equals the coefficient of the middle term, which is 10 .
| -24 | + | -1 | = | -25 | ||
| -12 | + | -2 | = | -14 | ||
| -8 | + | -3 | = | -11 | ||
| -6 | + | -4 | = | -10 | ||
| -4 | + | -6 | = | -10 | ||
| -3 | + | -8 | = | -11 | ||
| -2 | + | -12 | = | -14 | ||
| -1 | + | -24 | = | -25 | ||
| 1 | + | 24 | = | 25 | ||
| 2 | + | 12 | = | 14 | ||
| 3 | + | 8 | = | 11 | ||
| 4 | + | 6 | = | 10 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 4 and 6
8x2 + 4x + 6x + 3
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (2x+1)
Add up the last 2 terms, pulling out common factors :
3 • (2x+1)
Step-5 : Add up the four terms of step 4 :
(4x+3) • (2x+1)
Which is the desired factorization
Final result :
(2x + 1) • (4x + 3)
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