Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(22x2 + 8x) + 3
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 4x2+8x+3
The first term is, 4x2 its coefficient is 4 .
The middle term is, +8x its coefficient is 8 .
The last term, "the constant", is +3
Step-1 : Multiply the coefficient of the first term by the constant 4 • 3 = 12
Step-2 : Find two factors of 12 whose sum equals the coefficient of the middle term, which is 8 .
| -12 | + | -1 | = | -13 | ||
| -6 | + | -2 | = | -8 | ||
| -4 | + | -3 | = | -7 | ||
| -3 | + | -4 | = | -7 | ||
| -2 | + | -6 | = | -8 | ||
| -1 | + | -12 | = | -13 | ||
| 1 | + | 12 | = | 13 | ||
| 2 | + | 6 | = | 8 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 2 and 6
4x2 + 2x + 6x + 3
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (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 :
(2x+3) • (2x+1)
Which is the desired factorization
Final result :
(2x + 1) • (2x + 3)
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