Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(3x2 + 19x) + 20
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 3x2+19x+20
The first term is, 3x2 its coefficient is 3 .
The middle term is, +19x its coefficient is 19 .
The last term, "the constant", is +20
Step-1 : Multiply the coefficient of the first term by the constant 3 • 20 = 60
Step-2 : Find two factors of 60 whose sum equals the coefficient of the middle term, which is 19 .
| -60 | + | -1 | = | -61 | ||
| -30 | + | -2 | = | -32 | ||
| -20 | + | -3 | = | -23 | ||
| -15 | + | -4 | = | -19 | ||
| -12 | + | -5 | = | -17 | ||
| -10 | + | -6 | = | -16 | ||
| -6 | + | -10 | = | -16 | ||
| -5 | + | -12 | = | -17 | ||
| -4 | + | -15 | = | -19 | ||
| -3 | + | -20 | = | -23 | ||
| -2 | + | -30 | = | -32 | ||
| -1 | + | -60 | = | -61 | ||
| 1 | + | 60 | = | 61 | ||
| 2 | + | 30 | = | 32 | ||
| 3 | + | 20 | = | 23 | ||
| 4 | + | 15 | = | 19 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 4 and 15
3x2 + 4x + 15x + 20
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (3x+4)
Add up the last 2 terms, pulling out common factors :
5 • (3x+4)
Step-5 : Add up the four terms of step 4 :
(x+5) • (3x+4)
Which is the desired factorization
Final result :
(3x + 4) • (x + 5)
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