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)

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

f(-2) = -3f(1) = 6 . . . estimated from f(x) = (x+2)^2-3, which matches points on the graph (-1,-2) and (0, 1)

so the change in y-value for function f is (6 )) = 9.

the table tells us

g(-2) = 1g(1) = 31

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

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