Question

find factor x^2 − 120x + 3599

Answer 1

Answer:

The first term is, -x2 its coefficient is -1 .

The middle term is, +120x its coefficient is 120 .

The last term, "the constant", is +3600

Step-1 : Multiply the coefficient of the first term by the constant -1 • 3600 = -3600

Step-2 : Find two factors of -3600 whose sum equals the coefficient of the middle term, which is 120 .

-3600 + 1 = -3599

-1800 + 2 = -1798

-1200 + 3 = -1197

-900 + 4 = -896

-720 + 5 = -715

-600 + 6 = -594

For tidiness, printing of 39 lines which failed to find two such factors, was suppressed

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Step-by-step explanation:

Multiply both sides of the equation by (-1) to obtain positive coefficient for the first term:

x2-120x-3600 = 0 Add 3600 to both side of the equation :

x2-120x = 3600

Now the clever bit: Take the coefficient of x , which is 120 , divide by two, giving 60 , and finally square it giving 3600

Add 3600 to both sides of the equation :

On the right hand side we have :

3600 + 3600 or, (3600/1)+(3600/1)

The common denominator of the two fractions is 1 Adding (3600/1)+(3600/1) gives 7200/1

So adding to both sides we finally get :

x2-120x+3600 = 7200

Adding 3600 has completed the left hand side into a perfect square :

x2-120x+3600 =

(x-60) • (x-60) =

(x-60)2

Things which are equal to the same thing are also equal to one another. Since

x2-120x+3600 = 7200 and

x2-120x+3600 = (x-60)2

then, according to the law of transitivity,

(x-60)2 = 7200