Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(3x2 + 11x) - 20
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 3x2+11x-20
The first term is, 3x2 its coefficient is 3 .
The middle term is, +11x its coefficient is 11 .
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 11 .
| -60 | + | 1 | = | -59 | ||
| -30 | + | 2 | = | -28 | ||
| -20 | + | 3 | = | -17 | ||
| -15 | + | 4 | = | -11 | ||
| -12 | + | 5 | = | -7 | ||
| -10 | + | 6 | = | -4 | ||
| -6 | + | 10 | = | 4 | ||
| -5 | + | 12 | = | 7 | ||
| -4 | + | 15 | = | 11 | 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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