8x²-70x+750 solve it by splliting the middle term
Answers
Answer:
Step-by-step explanation:
8x2-70x-750
Final result :
2 • (x - 15) • (4x + 25)
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(23x2 - 70x) - 750
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
8x2 - 70x - 750 = 2 • (4x2 - 35x - 375)
Trying to factor by splitting the middle term
3.2 Factoring 4x2 - 35x - 375
The first term is, 4x2 its coefficient is 4 .
The middle term is, -35x its coefficient is -35 .
The last term, "the constant", is -375
Step-1 : Multiply the coefficient of the first term by the constant 4 • -375 = -1500
Step-2 : Find two factors of -1500 whose sum equals the coefficient of the middle term, which is -35 .
-1500 + 1 = -1499
-750 + 2 = -748
-500 + 3 = -497
-375 + 4 = -371
-300 + 5 = -295
-250 + 6 = -244
-150 + 10 = -140
-125 + 12 = -113
-100 + 15 = -85
-75 + 20 = -55
-60 + 25 = -35 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -60 and 25
4x2 - 60x + 25x - 375
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (x-15)
Add up the last 2 terms, pulling out common factors :
25 • (x-15)
Step-5 : Add up the four terms of step 4 :
(4x+25) • (x-15)
Which is the desired factorization
Final result :
2 • (x - 15) • (4x + 25)