Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(24x2 + 54x) - 7
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 16x2+54x-7
The first term is, 16x2 its coefficient is 16 .
The middle term is, +54x its coefficient is 54 .
The last term, "the constant", is -7
Step-1 : Multiply the coefficient of the first term by the constant 16 • -7 = -112
Step-2 : Find two factors of -112 whose sum equals the coefficient of the middle term, which is 54 .
| -112 | + | 1 | = | -111 | ||
| -56 | + | 2 | = | -54 | ||
| -28 | + | 4 | = | -24 | ||
| -16 | + | 7 | = | -9 | ||
| -14 | + | 8 | = | -6 | ||
| -8 | + | 14 | = | 6 | ||
| -7 | + | 16 | = | 9 | ||
| -4 | + | 28 | = | 24 | ||
| -2 | + | 56 | = | 54 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 56
16x2 - 2x + 56x - 7
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (8x-1)
Add up the last 2 terms, pulling out common factors :
7 • (8x-1)
Step-5 : Add up the four terms of step 4 :
(2x+7) • (8x-1)
Which is the desired factorization
Final result :
(8x - 1) • (2x + 7)
How did we do?
Please leave us feedback.