Question

12x^2-x-35

Answer 1

12x2-x-35



Step by step solution :

Step 1 :
Simplify 12x^2-x - 35


Trying to factor by splitting the middle term

1.1 Factoring 12x2-x-35

The first term is, 12x2 its coefficient is 12 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -35

Step-1 : Multiply the coefficient of the first term by the constant 12 • -35 = -420

Step-2 : Find two factors of -420 whose sum equals the coefficient of the middle term, which is -1 .


-420 + 1 = -419
-210 + 2 = -208
-140 + 3 = -137
-105 + 4 = -101
-84 + 5 = -79
-70 + 6 = -64
-60 + 7 = -53
-42 + 10 = -32
-35 + 12 = -23
-30 + 14 = -16
-28 + 15 = -13
-21 + 20 = -1 That's it


Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -21 and 20
12x2 - 21x + 20x - 35

Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (4x-7)
Add up the last 2 terms, pulling out common factors :
5 • (4x-7)
Now add up the four terms of step 3 :
(3x+5) • (4x-7)
Which is the desired factorization

Final result :
(4x - 7) • (3x + 5)