Solution - Simplification or other simple results
Other Ways to Solve:
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((x2)+8x)-(((0-3x2)-3x)-7)
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 4x2+11x+7
The first term is, 4x2 its coefficient is 4 .
The middle term is, +11x its coefficient is 11 .
The last term, "the constant", is +7
Step-1 : Multiply the coefficient of the first term by the constant 4 • 7 = 28
Step-2 : Find two factors of 28 whose sum equals the coefficient of the middle term, which is 11 .
| -28 | + | -1 | = | -29 | ||
| -14 | + | -2 | = | -16 | ||
| -7 | + | -4 | = | -11 | ||
| -4 | + | -7 | = | -11 | ||
| -2 | + | -14 | = | -16 | ||
| -1 | + | -28 | = | -29 | ||
| 1 | + | 28 | = | 29 | ||
| 2 | + | 14 | = | 16 | ||
| 4 | + | 7 | = | 11 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 4 and 7
4x2 + 4x + 7x + 7
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (x+1)
Add up the last 2 terms, pulling out common factors :
7 • (x+1)
Step-5 : Add up the four terms of step 4 :
(4x+7) • (x+1)
Which is the desired factorization
Final result :
(x + 1) • (4x + 7)
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