Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(5x2 + 29x) + 20
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 5x2+29x+20
The first term is, 5x2 its coefficient is 5 .
The middle term is, +29x its coefficient is 29 .
The last term, "the constant", is +20
Step-1 : Multiply the coefficient of the first term by the constant 5 • 20 = 100
Step-2 : Find two factors of 100 whose sum equals the coefficient of the middle term, which is 29 .
| -100 | + | -1 | = | -101 | ||
| -50 | + | -2 | = | -52 | ||
| -25 | + | -4 | = | -29 | ||
| -20 | + | -5 | = | -25 | ||
| -10 | + | -10 | = | -20 | ||
| -5 | + | -20 | = | -25 | ||
| -4 | + | -25 | = | -29 | ||
| -2 | + | -50 | = | -52 | ||
| -1 | + | -100 | = | -101 | ||
| 1 | + | 100 | = | 101 | ||
| 2 | + | 50 | = | 52 | ||
| 4 | + | 25 | = | 29 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 4 and 25
5x2 + 4x + 25x + 20
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (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 :
(x+5) • (5x+4)
Which is the desired factorization
Final result :
(5x + 4) • (x + 5)
How did we do?
Please leave us feedback.