Answer :
The value of c is a true zero of the polynomial function P(x)
How to show that c is a zero of the polynomial?
The polynomial function is given as
P(x) = x³ + 3x² - 16x - 48
Also, we have the value of c to be
c = -3
If truly, the variable c is a zero of the polynomial, then the following must be true
P(c) = 0
Start by substituting -3 for c in the equation P(x) = x³ + 3x² - 16x - 48
So, we have
P(-3) = (-3)³ + 3(-3)² - 16(-3) - 48
Evaluate the exponents
P(-3) = -27 + 3(9) - 16(-3) - 48
Evaluate the products
P(-3) = -27 + 27 + 48 - 48
Evaluate the sum and the difference
P(-3) = 0
Recall that
c = -3
So, we have
P(c) = 0
Hence, c is a zero of the polynomial because P(c) = 0
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