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30 points
need
explain as much as possible

A Yes

The polynomial remainder theorem says when we divide polynomial f(x) by x-a we'll get remainder f(a).

f(x)=x^3-3x^2-31x-72

f(8)=8^3-3(8^2)-31(8)-72

f(8)=512-3(64)-31(8)- 72 = 512-192-248-72= 0

Since f(8)=0 that means x-8 has a remainder zero when divided by f(x).  In other words, it's a factor of f(x).

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.