Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(5x2 + 42x) + 49
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 5x2+42x+49
The first term is, 5x2 its coefficient is 5 .
The middle term is, +42x its coefficient is 42 .
The last term, "the constant", is +49
Step-1 : Multiply the coefficient of the first term by the constant 5 • 49 = 245
Step-2 : Find two factors of 245 whose sum equals the coefficient of the middle term, which is 42 .
| -245 | + | -1 | = | -246 | ||
| -49 | + | -5 | = | -54 | ||
| -35 | + | -7 | = | -42 | ||
| -7 | + | -35 | = | -42 | ||
| -5 | + | -49 | = | -54 | ||
| -1 | + | -245 | = | -246 | ||
| 1 | + | 245 | = | 246 | ||
| 5 | + | 49 | = | 54 | ||
| 7 | + | 35 | = | 42 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 7 and 35
5x2 + 7x + 35x + 49
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (5x+7)
Add up the last 2 terms, pulling out common factors :
7 • (5x+7)
Step-5 : Add up the four terms of step 4 :
(x+7) • (5x+7)
Which is the desired factorization
Final result :
(5x + 7) • (x + 7)
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