Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(5x2 + 28x) + 15
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 5x2+28x+15
The first term is, 5x2 its coefficient is 5 .
The middle term is, +28x its coefficient is 28 .
The last term, "the constant", is +15
Step-1 : Multiply the coefficient of the first term by the constant 5 • 15 = 75
Step-2 : Find two factors of 75 whose sum equals the coefficient of the middle term, which is 28 .
| -75 | + | -1 | = | -76 | ||
| -25 | + | -3 | = | -28 | ||
| -15 | + | -5 | = | -20 | ||
| -5 | + | -15 | = | -20 | ||
| -3 | + | -25 | = | -28 | ||
| -1 | + | -75 | = | -76 | ||
| 1 | + | 75 | = | 76 | ||
| 3 | + | 25 | = | 28 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 3 and 25
5x2 + 3x + 25x + 15
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (5x+3)
Add up the last 2 terms, pulling out common factors :
5 • (5x+3)
Step-5 : Add up the four terms of step 4 :
(x+5) • (5x+3)
Which is the desired factorization
Final result :
(5x + 3) • (x + 5)
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