Question

x^2 + 40x - 32000 = 0 factorize the equation​

Answer 1

term

1.1 Factoring x2+40x-32000

The first term is, x2 its coefficient is 1 .

The middle term is, +40x its coefficient is 40 .

The last term, "the constant", is -32000

Step-1 : Multiply the coefficient of the first term by the constant 1 • -32000 = -32000

Step-2 : Find two factors of -32000 whose sum equals the coefficient of the middle term, which is 40 .

-32000 + 1 = -31999

-16000 + 2 = -15998

-8000 + 4 = -7996

-6400 + 5 = -6395

-4000 + 8 = -3992

-3200 + 10 = -3190

-2000 + 16 = -1984

-1600 + 20 = -1580

-1280 + 25 = -1255

-1000 + 32 = -968

-800 + 40 = -760

-640 + 50 = -590

-500 + 64 = -436

-400 + 80 = -320

-320 + 100 = -220

-256 + 125 = -131

-250 + 128 = -122

-200 + 160 = -40

-160 + 200 = 40 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -160 and 200

x2 - 160x + 200x - 32000

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

x • (x-160)

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

200 • (x-160)

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

(x+200) • (x-160)

Which is the desired factorization