Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((3•5x2) + 64x) + 64
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 15x2+64x+64
The first term is, 15x2 its coefficient is 15 .
The middle term is, +64x its coefficient is 64 .
The last term, "the constant", is +64
Step-1 : Multiply the coefficient of the first term by the constant 15 • 64 = 960
Step-2 : Find two factors of 960 whose sum equals the coefficient of the middle term, which is 64 .
| -960 | + | -1 | = | -961 | ||
| -480 | + | -2 | = | -482 | ||
| -320 | + | -3 | = | -323 | ||
| -240 | + | -4 | = | -244 | ||
| -192 | + | -5 | = | -197 | ||
| -160 | + | -6 | = | -166 | ||
| -120 | + | -8 | = | -128 | ||
| -96 | + | -10 | = | -106 | ||
| -80 | + | -12 | = | -92 | ||
| -64 | + | -15 | = | -79 | ||
| -60 | + | -16 | = | -76 | ||
| -48 | + | -20 | = | -68 | ||
| -40 | + | -24 | = | -64 | ||
| -32 | + | -30 | = | -62 | ||
| -30 | + | -32 | = | -62 | ||
| -24 | + | -40 | = | -64 | ||
| -20 | + | -48 | = | -68 | ||
| -16 | + | -60 | = | -76 | ||
| -15 | + | -64 | = | -79 | ||
| -12 | + | -80 | = | -92 | ||
| -10 | + | -96 | = | -106 | ||
| -8 | + | -120 | = | -128 | ||
| -6 | + | -160 | = | -166 | ||
| -5 | + | -192 | = | -197 | ||
| -4 | + | -240 | = | -244 | ||
| -3 | + | -320 | = | -323 | ||
| -2 | + | -480 | = | -482 | ||
| -1 | + | -960 | = | -961 | ||
| 1 | + | 960 | = | 961 | ||
| 2 | + | 480 | = | 482 | ||
| 3 | + | 320 | = | 323 | ||
| 4 | + | 240 | = | 244 | ||
| 5 | + | 192 | = | 197 | ||
| 6 | + | 160 | = | 166 | ||
| 8 | + | 120 | = | 128 | ||
| 10 | + | 96 | = | 106 | ||
| 12 | + | 80 | = | 92 | ||
| 15 | + | 64 | = | 79 | ||
| 16 | + | 60 | = | 76 | ||
| 20 | + | 48 | = | 68 | ||
| 24 | + | 40 | = | 64 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 24 and 40
15x2 + 24x + 40x + 64
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (5x+8)
Add up the last 2 terms, pulling out common factors :
8 • (5x+8)
Step-5 : Add up the four terms of step 4 :
(3x+8) • (5x+8)
Which is the desired factorization
Final result :
(5x + 8) • (3x + 8)
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