Which binomial is not a devisor of x^3-11x^2+16x+84?

dividend x3 - 11x2 + 16x + 84 - divisor * x2 x3 - 7x2 remainder - 4x2 + 16x + 84 - divisor * - 4x1 - 4x2 + 28x remainder - 12x + 84 - divisor * - 12x0 - 12x + 84 remainder 0 Quotient : x2-4x-12 Remainder: 0 Step-1 : Multiply the coefficient of the first term by the constant 1 • - 12 = - 12 Step-2 : Find two factors of - 12 whose sum equals the coefficient of the middle term, which is - 4. - 12 + 1 = - 11 - 6 + 2 = - 4 That's it Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, - 6 and 2 x2 - 6x + 2x - 12 Step-4 : Add up the first 2 terms, pulling out like factors : x • (x-6) Add up the last 2 terms, pulling out common factors : 2 • (x-6) Step-5 : Add up the four terms of step 4 : (x+2) • (x-6) Which is the desired factorization Final result : (x + 2) • (x - 6) • (x - 7)