Solution - Simplification or other simple results
Other Ways to Solve:
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(24x2 + 8x) - 15
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 16x2+8x-15
The first term is, 16x2 its coefficient is 16 .
The middle term is, +8x its coefficient is 8 .
The last term, "the constant", is -15
Step-1 : Multiply the coefficient of the first term by the constant 16 • -15 = -240
Step-2 : Find two factors of -240 whose sum equals the coefficient of the middle term, which is 8 .
| -240 | + | 1 | = | -239 | ||
| -120 | + | 2 | = | -118 | ||
| -80 | + | 3 | = | -77 | ||
| -60 | + | 4 | = | -56 | ||
| -48 | + | 5 | = | -43 | ||
| -40 | + | 6 | = | -34 | ||
| -30 | + | 8 | = | -22 | ||
| -24 | + | 10 | = | -14 | ||
| -20 | + | 12 | = | -8 | ||
| -16 | + | 15 | = | -1 | ||
| -15 | + | 16 | = | 1 | ||
| -12 | + | 20 | = | 8 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and 20
16x2 - 12x + 20x - 15
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (4x-3)
Add up the last 2 terms, pulling out common factors :
5 • (4x-3)
Step-5 : Add up the four terms of step 4 :
(4x+5) • (4x-3)
Which is the desired factorization
Final result :
(4x - 3) • (4x + 5)
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