Question

Factorise 12 (4x- 1/4x )²+5(4x-1/4x)-2%E2%80%8B​

Answer 1

Step-by-step explanation:

Factoring 675x2 + 75x - 8

The first term is, 675x2 its coefficient is 675 .

The middle term is, +75x its coefficient is 75 .

The last term, "the constant", is -8

Step-1 : Multiply the coefficient of the first term by the constant 675 • -8 = -5400

Step-2 : Find two factors of -5400 whose sum equals the coefficient of the middle term, which is 75 .

-5400 + 1 = -5399

-2700 + 2 = -2698

-1800 + 3 = -1797

-1350 + 4 = -1346

-1080 + 5 = -1075

-900 + 6 = -894

-675 + 8 = -667

-600 + 9 = -591

-540 + 10 = -530

-450 + 12 = -438

-360 + 15 = -345

-300 + 18 = -282

-270 + 20 = -250

-225 + 24 = -201

-216 + 25 = -191

-200 + 27 = -173

-180 + 30 = -150

-150 + 36 = -114

-135 + 40 = -95

-120 + 45 = -75

-108 + 50 = -58

-100 + 54 = -46

-90 + 60 = -30

-75 + 72 = -3

-72 + 75 = 3

-60 + 90 = 30

-54 + 100 = 46

-50 + 108 = 58

-45 + 120 = 75 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -45 and 120

675x2 - 45x + 120x - 8

Step-4 : Add up the first 2 terms, pulling out like factors :

45x • (15x-1)

Add up the last 2 terms, pulling out common factors :

8 • (15x-1)

Step-5 : Add up the four terms of step 4 :

(45x+8) • (15x-1)

Which is the desired factorization