Question

59 n 2+61n-7140
do by splitting the middle term

Answer 1

Answer:

The first term is, n2 its coefficient is 1 .

The middle term is, -61n its coefficient is -61 .

The last term, "the constant", is +900

Step-1 : Multiply the coefficient of the first term by the constant 1 • 900 = 900

Step-2 : Find two factors of 900 whose sum equals the coefficient of the middle term, which is -61 .

-900 + -1 = -901

-450 + -2 = -452

-300 + -3 = -303

-225 + -4 = -229

-180 + -5 = -185

-150 + -6 = -156

-100 + -9 = -109

-90 + -10 = -100

-75 + -12 = -87

-60 + -15 = -75

-50 + -18 = -68

-45 + -20 = -65

-36 + -25 = -61 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -36 and -25

n2 - 36n - 25n - 900

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

n • (n-36)

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

25 • (n-36)

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

(n-25) • (n-36)

Which is the desired factorization

Equation at the end of step

1

:

(n - 25) • (n - 36) = 0