Question

Factorise

x^2-40x+384=0​

Answer 1

Answer:

Factoring x2-40x+384

The first term is, x2 its coefficient is 1 .

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

The last term, "the constant", is +384

Step-1 : Multiply the coefficient of the first term by the constant 1 • 384 = 384

Step-2 : Find two factors of 384 whose sum equals the coefficient of the middle term, which is -40 .

-384 + -1 = -385

-192 + -2 = -194

-128 + -3 = -131

-96 + -4 = -100

-64 + -6 = -70

-48 + -8 = -56

-32 + -12 = -44

-24 + -16 = -40 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -24 and -16

x2 - 24x - 16x - 384

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

x • (x-24)

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

16 • (x-24)

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

(x-16) • (x-24)

Which is the desired factorization