Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(23x2 + 26x) + 20
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
8x2 + 26x + 20 = 2 • (4x2 + 13x + 10)
Trying to factor by splitting the middle term
3.2 Factoring 4x2 + 13x + 10
The first term is, 4x2 its coefficient is 4 .
The middle term is, +13x its coefficient is 13 .
The last term, "the constant", is +10
Step-1 : Multiply the coefficient of the first term by the constant 4 • 10 = 40
Step-2 : Find two factors of 40 whose sum equals the coefficient of the middle term, which is 13 .
| -40 | + | -1 | = | -41 | ||
| -20 | + | -2 | = | -22 | ||
| -10 | + | -4 | = | -14 | ||
| -8 | + | -5 | = | -13 | ||
| -5 | + | -8 | = | -13 | ||
| -4 | + | -10 | = | -14 | ||
| -2 | + | -20 | = | -22 | ||
| -1 | + | -40 | = | -41 | ||
| 1 | + | 40 | = | 41 | ||
| 2 | + | 20 | = | 22 | ||
| 4 | + | 10 | = | 14 | ||
| 5 | + | 8 | = | 13 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 5 and 8
4x2 + 5x + 8x + 10
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (4x+5)
Add up the last 2 terms, pulling out common factors :
2 • (4x+5)
Step-5 : Add up the four terms of step 4 :
(x+2) • (4x+5)
Which is the desired factorization
Final result :
2 • (4x + 5) • (x + 2)
How did we do?
Please leave us feedback.