Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((0 - 7x2) - 24x) - 9
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
-7x2 - 24x - 9 = -1 • (7x2 + 24x + 9)
Trying to factor by splitting the middle term
3.2 Factoring 7x2 + 24x + 9
The first term is, 7x2 its coefficient is 7 .
The middle term is, +24x its coefficient is 24 .
The last term, "the constant", is +9
Step-1 : Multiply the coefficient of the first term by the constant 7 • 9 = 63
Step-2 : Find two factors of 63 whose sum equals the coefficient of the middle term, which is 24 .
| -63 | + | -1 | = | -64 | ||
| -21 | + | -3 | = | -24 | ||
| -9 | + | -7 | = | -16 | ||
| -7 | + | -9 | = | -16 | ||
| -3 | + | -21 | = | -24 | ||
| -1 | + | -63 | = | -64 | ||
| 1 | + | 63 | = | 64 | ||
| 3 | + | 21 | = | 24 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 3 and 21
7x2 + 3x + 21x + 9
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (7x+3)
Add up the last 2 terms, pulling out common factors :
3 • (7x+3)
Step-5 : Add up the four terms of step 4 :
(x+3) • (7x+3)
Which is the desired factorization
Final result :
(-7x - 3) • (x + 3)
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