Find the value of c so that (x+2) is a factor of the polynomial p(x). p(x)=4x^3+cx^2+x+2

c = 8

Step-by-step explanation:

Use synthetic division here; it's the fastest approach.

Given that (x + 2) is a factor, take -2 and use this as the divisor in synthetic division:

-2     4         c                1           2

                  -8    (-2c+ 16)      (4c-34)

         4    (c - 8)   (-2c + 17)     4c - 32

The remainder, 4c - 32, must equal zero if (x + 2) is a factor.

Then 4c - 32 = 0, and c = 8

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step-by-step explanation: