Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(22x2 + 12x) + 5
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 4x2+12x+5
The first term is, 4x2 its coefficient is 4 .
The middle term is, +12x its coefficient is 12 .
The last term, "the constant", is +5
Step-1 : Multiply the coefficient of the first term by the constant 4 • 5 = 20
Step-2 : Find two factors of 20 whose sum equals the coefficient of the middle term, which is 12 .
| -20 | + | -1 | = | -21 | ||
| -10 | + | -2 | = | -12 | ||
| -5 | + | -4 | = | -9 | ||
| -4 | + | -5 | = | -9 | ||
| -2 | + | -10 | = | -12 | ||
| -1 | + | -20 | = | -21 | ||
| 1 | + | 20 | = | 21 | ||
| 2 | + | 10 | = | 12 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 2 and 10
4x2 + 2x + 10x + 5
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (2x+1)
Add up the last 2 terms, pulling out common factors :
5 • (2x+1)
Step-5 : Add up the four terms of step 4 :
(2x+5) • (2x+1)
Which is the desired factorization
Final result :
(2x + 1) • (2x + 5)
How did we do?
Please leave us feedback.