63x²+101x+40
resolve into factor
Answers
Answer:
Factoring 63x2+101x+40
The first term is, 63x2 its coefficient is 63 .
The middle term is, +101x its coefficient is 101 .
The last term, "the constant", is +40
Step-1 : Multiply the coefficient of the first term by the constant 63 • 40 = 2520
Step-2 : Find two factors of 2520 whose sum equals the coefficient of the middle term, which is 101 .
-2520 + -1 = -2521
-1260 + -2 = -1262
-840 + -3 = -843
-630 + -4 = -634
-504 + -5 = -509
-420 + -6 = -426
-360 + -7 = -367
-315 + -8 = -323
-280 + -9 = -289
-252 + -10 = -262
-210 + -12 = -222
-180 + -14 = -194
-168 + -15 = -183
-140 + -18 = -158
-126 + -20 = -146
-120 + -21 = -141
-105 + -24 = -129
-90 + -28 = -118
-84 + -30 = -114
-72 + -35 = -107
-70 + -36 = -106
-63 + -40 = -103
-60 + -42 = -102
-56 + -45 = -101
-45 + -56 = -101
-42 + -60 = -102
-40 + -63 = -103
-36 + -70 = -106
-35 + -72 = -107
-30 + -84 = -114
-28 + -90 = -118
-24 + -105 = -129
-21 + -120 = -141
-20 + -126 = -146
-18 + -140 = -158
-15 + -168 = -183
-14 + -180 = -194
-12 + -210 = -222
-10 + -252 = -262
-9 + -280 = -289
-8 + -315 = -323
-7 + -360 = -367
-6 + -420 = -426
-5 + -504 = -509
-4 + -630 = -634
-3 + -840 = -843
-2 + -1260 = -1262
-1 + -2520 = -2521
1 + 2520 = 2521
2 + 1260 = 1262
3 + 840 = 843
4 + 630 = 634
5 + 504 = 509
6 + 420 = 426
7 + 360 = 367
8 + 315 = 323
9 + 280 = 289
10 + 252 = 262
12 + 210 = 222
14 + 180 = 194
15 + 168 = 183
18 + 140 = 158
20 + 126 = 146
21 + 120 = 141
24 + 105 = 129
28 + 90 = 118
30 + 84 = 114
35 + 72 = 107
36 + 70 = 106
40 + 63 = 103
42 + 60 = 102
45 + 56 = 101 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 45 and 56
63x2 + 45x + 56x + 40
Step-4 : Add up the first 2 terms, pulling out like factors :
9x • (7x+5)
Add up the last 2 terms, pulling out common Factors
8 • (7x+5)
Step-5 : Add up the four terms of step 4 :
(9x+8) • (7x+5)
Which is the desired factorization
Final result :
(7x + 5) • (9x + 8)
Hope it helps
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