The equation of the polynomial equation from the properties is P(x) = 8/15(x + 3)(x + 1)(x - 5)
<h3>How to determine the polynomial expression from the stated properties?</h3>
The given parameters are
Degree = third degree
Zero = -3, -1 and 5
y-intercept = -8
There are no complex numbers in the above zeros
This means that, the given zeros are the only zeros of the polynomial
i.e Zero = -3, -1 and 5
The equation of the polynomial is then calculated as
P(x) = Leading coefficient * (x - zero)^multiplicity
So, we have
P(x) = a * (x - (-3)) * (x - (-1)) * (x - 5)
This gives
P(x) = a * (x + 3) * (x + 1) * (x - 5)
The y-intercept is -8
This means that
P(0) = -8
i.e. when x = 0, P(x) = -8
So, we have the following representation
a * (0 + 3) * (0 + 1) * (0 - 5) = -8
Evaluate the products
So, we have the following representation
a * -15 = -8
Divide both sides by -5
a = 8/15
Substitute a = 8/15 in P(x) = a * (x + 3) * (x + 1) * (x - 5)
P(x) = 8/15 * (x + 3) * (x + 1) * (x - 5)
So, we have
P(x) = 8/15(x + 3)(x + 1)(x - 5)
Hence, the equation is P(x) = 8/15(x + 3)(x + 1)(x - 5)
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brainly.com/question/17517586
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