Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((3•5x2) + 37x) + 20
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 15x2+37x+20
The first term is, 15x2 its coefficient is 15 .
The middle term is, +37x its coefficient is 37 .
The last term, "the constant", is +20
Step-1 : Multiply the coefficient of the first term by the constant 15 • 20 = 300
Step-2 : Find two factors of 300 whose sum equals the coefficient of the middle term, which is 37 .
| -300 | + | -1 | = | -301 | ||
| -150 | + | -2 | = | -152 | ||
| -100 | + | -3 | = | -103 | ||
| -75 | + | -4 | = | -79 | ||
| -60 | + | -5 | = | -65 | ||
| -50 | + | -6 | = | -56 | ||
| -30 | + | -10 | = | -40 | ||
| -25 | + | -12 | = | -37 | ||
| -20 | + | -15 | = | -35 | ||
| -15 | + | -20 | = | -35 | ||
| -12 | + | -25 | = | -37 | ||
| -10 | + | -30 | = | -40 | ||
| -6 | + | -50 | = | -56 | ||
| -5 | + | -60 | = | -65 | ||
| -4 | + | -75 | = | -79 | ||
| -3 | + | -100 | = | -103 | ||
| -2 | + | -150 | = | -152 | ||
| -1 | + | -300 | = | -301 | ||
| 1 | + | 300 | = | 301 | ||
| 2 | + | 150 | = | 152 | ||
| 3 | + | 100 | = | 103 | ||
| 4 | + | 75 | = | 79 | ||
| 5 | + | 60 | = | 65 | ||
| 6 | + | 50 | = | 56 | ||
| 10 | + | 30 | = | 40 | ||
| 12 | + | 25 | = | 37 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 12 and 25
15x2 + 12x + 25x + 20
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (5x+4)
Add up the last 2 terms, pulling out common factors :
5 • (5x+4)
Step-5 : Add up the four terms of step 4 :
(3x+5) • (5x+4)
Which is the desired factorization
Final result :
(5x + 4) • (3x + 5)
How did we do?
Please leave us feedback.