Suppose you need to graph the function f(x) = x(4x + 7)(x - 1)^7. Are there going to be any repeated zeros?

yes

Step-by-step explanation:

hello,

as we have

the zero 1 is repeated 7 times

hope this helps

  yes

Step-by-step explanation:

The exponent on each factor tells you the number of times it is repeated. The zero represented by the factor (x -1)⁷ is repeated 7 times.

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When a zero is repeated, the graph is flattened there. The more times it is repeated, the "flatter" the function is at that point. If the repeat-count is even, the graph touches the axis, but does not cross. Here, the repeat-count is odd, so the graph flattens out at the x-intercept, and crosses the x-axis.

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18