Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(3x2 + 5x) + 2
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 3x2+5x+2
The first term is, 3x2 its coefficient is 3 .
The middle term is, +5x its coefficient is 5 .
The last term, "the constant", is +2
Step-1 : Multiply the coefficient of the first term by the constant 3 • 2 = 6
Step-2 : Find two factors of 6 whose sum equals the coefficient of the middle term, which is 5 .
| -6 | + | -1 | = | -7 | ||
| -3 | + | -2 | = | -5 | ||
| -2 | + | -3 | = | -5 | ||
| -1 | + | -6 | = | -7 | ||
| 1 | + | 6 | = | 7 | ||
| 2 | + | 3 | = | 5 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 2 and 3
3x2 + 2x + 3x + 2
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (3x+2)
Add up the last 2 terms, pulling out common factors :
1 • (3x+2)
Step-5 : Add up the four terms of step 4 :
(x+1) • (3x+2)
Which is the desired factorization
Final result :
(3x + 2) • (x + 1)
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