Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(3x2 + 16x) + 5
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 3x2+16x+5
The first term is, 3x2 its coefficient is 3 .
The middle term is, +16x its coefficient is 16 .
The last term, "the constant", is +5
Step-1 : Multiply the coefficient of the first term by the constant 3 • 5 = 15
Step-2 : Find two factors of 15 whose sum equals the coefficient of the middle term, which is 16 .
| -15 | + | -1 | = | -16 | ||
| -5 | + | -3 | = | -8 | ||
| -3 | + | -5 | = | -8 | ||
| -1 | + | -15 | = | -16 | ||
| 1 | + | 15 | = | 16 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 1 and 15
3x2 + 1x + 15x + 5
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (3x+1)
Add up the last 2 terms, pulling out common factors :
5 • (3x+1)
Step-5 : Add up the four terms of step 4 :
(x+5) • (3x+1)
Which is the desired factorization
Final result :
(3x + 1) • (x + 5)
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