Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(5x2 + 26x) + 24
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 5x2+26x+24
The first term is, 5x2 its coefficient is 5 .
The middle term is, +26x its coefficient is 26 .
The last term, "the constant", is +24
Step-1 : Multiply the coefficient of the first term by the constant 5 • 24 = 120
Step-2 : Find two factors of 120 whose sum equals the coefficient of the middle term, which is 26 .
| -120 | + | -1 | = | -121 | ||
| -60 | + | -2 | = | -62 | ||
| -40 | + | -3 | = | -43 | ||
| -30 | + | -4 | = | -34 | ||
| -24 | + | -5 | = | -29 | ||
| -20 | + | -6 | = | -26 | ||
| -15 | + | -8 | = | -23 | ||
| -12 | + | -10 | = | -22 | ||
| -10 | + | -12 | = | -22 | ||
| -8 | + | -15 | = | -23 | ||
| -6 | + | -20 | = | -26 | ||
| -5 | + | -24 | = | -29 | ||
| -4 | + | -30 | = | -34 | ||
| -3 | + | -40 | = | -43 | ||
| -2 | + | -60 | = | -62 | ||
| -1 | + | -120 | = | -121 | ||
| 1 | + | 120 | = | 121 | ||
| 2 | + | 60 | = | 62 | ||
| 3 | + | 40 | = | 43 | ||
| 4 | + | 30 | = | 34 | ||
| 5 | + | 24 | = | 29 | ||
| 6 | + | 20 | = | 26 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 6 and 20
5x2 + 6x + 20x + 24
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (5x+6)
Add up the last 2 terms, pulling out common factors :
4 • (5x+6)
Step-5 : Add up the four terms of step 4 :
(x+4) • (5x+6)
Which is the desired factorization
Final result :
(5x + 6) • (x + 4)
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