Factor (x) into linear factors given that k is a zero of f(x)

Factored form (linear): (4x+3)(x-3)(x-5)

Step-by-step explanation:

Using long division and factoring, we can find the answer. Since the root/zero of 5 is given already, we can change this into a factor of (x - 5) as 5 is a root.

Step 1: Long division. Divide f(x) by (x-5)

Once you do long division, you should have left over (x-5)(4x²+9x-9)

Step 2: Factor the quadratic

Since you can't do gcf, you have to leave the 4x as a factor. Once you factor out the quadratic, you should get the

(x-5)(4x+3)(x-3)

Step 3: Rearrange (Optional)

(4x+3)(x-3)(x-5)

last one.

step-by-step explanation:

last one.

generally speaking, the others follow some sort of pattern that correlates to either linear (looks like a straight line) or sinusoidal (looks like an s).

the last one is just a random cloud of points that doesn't correlate to any particular known order.

  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.

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

the table tells us

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).