Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring z2+10z+21
The first term is, z2 its coefficient is 1 .
The middle term is, +10z its coefficient is 10 .
The last term, "the constant", is +21
Step-1 : Multiply the coefficient of the first term by the constant 1 • 21 = 21
Step-2 : Find two factors of 21 whose sum equals the coefficient of the middle term, which is 10 .
| -21 | + | -1 | = | -22 | ||
| -7 | + | -3 | = | -10 | ||
| -3 | + | -7 | = | -10 | ||
| -1 | + | -21 | = | -22 | ||
| 1 | + | 21 | = | 22 | ||
| 3 | + | 7 | = | 10 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 3 and 7
z2 + 3z + 7z + 21
Step-4 : Add up the first 2 terms, pulling out like factors :
z • (z+3)
Add up the last 2 terms, pulling out common factors :
7 • (z+3)
Step-5 : Add up the four terms of step 4 :
(z+7) • (z+3)
Which is the desired factorization
Final result :
(z + 7) • (z + 3)
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