Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(5x2 + 21x) + 4
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 5x2+21x+4
The first term is, 5x2 its coefficient is 5 .
The middle term is, +21x its coefficient is 21 .
The last term, "the constant", is +4
Step-1 : Multiply the coefficient of the first term by the constant 5 • 4 = 20
Step-2 : Find two factors of 20 whose sum equals the coefficient of the middle term, which is 21 .
| -20 | + | -1 | = | -21 | ||
| -10 | + | -2 | = | -12 | ||
| -5 | + | -4 | = | -9 | ||
| -4 | + | -5 | = | -9 | ||
| -2 | + | -10 | = | -12 | ||
| -1 | + | -20 | = | -21 | ||
| 1 | + | 20 | = | 21 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 1 and 20
5x2 + 1x + 20x + 4
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (5x+1)
Add up the last 2 terms, pulling out common factors :
4 • (5x+1)
Step-5 : Add up the four terms of step 4 :
(x+4) • (5x+1)
Which is the desired factorization
Final result :
(5x + 1) • (x + 4)
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