Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(24x2 + 41x) - 21
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 16x2+41x-21
The first term is, 16x2 its coefficient is 16 .
The middle term is, +41x its coefficient is 41 .
The last term, "the constant", is -21
Step-1 : Multiply the coefficient of the first term by the constant 16 • -21 = -336
Step-2 : Find two factors of -336 whose sum equals the coefficient of the middle term, which is 41 .
| -336 | + | 1 | = | -335 | ||
| -168 | + | 2 | = | -166 | ||
| -112 | + | 3 | = | -109 | ||
| -84 | + | 4 | = | -80 | ||
| -56 | + | 6 | = | -50 | ||
| -48 | + | 7 | = | -41 | ||
| -42 | + | 8 | = | -34 | ||
| -28 | + | 12 | = | -16 | ||
| -24 | + | 14 | = | -10 | ||
| -21 | + | 16 | = | -5 | ||
| -16 | + | 21 | = | 5 | ||
| -14 | + | 24 | = | 10 | ||
| -12 | + | 28 | = | 16 | ||
| -8 | + | 42 | = | 34 | ||
| -7 | + | 48 | = | 41 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and 48
16x2 - 7x + 48x - 21
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (16x-7)
Add up the last 2 terms, pulling out common factors :
3 • (16x-7)
Step-5 : Add up the four terms of step 4 :
(x+3) • (16x-7)
Which is the desired factorization
Final result :
(16x - 7) • (x + 3)
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