The equation of the polynomial in standard form is f(x) = x⁴ - 12x³ + 48x² - 64x
Polynomial is an expression that involves only the operations of addition, subtraction, multiplication of variables.
Given that a polynomial function has a zero at 4 (multiplicity 3) and 0 (multiplicity 1).
Let f(x) represent the polynomial.
Hence: x = 4, x = 4, x = 4, x = 0
x - 4 = 0, x - 4 = 0, x - 4 = 0, x = 0
f(x) = (x - 4)(x - 4)(x -4)(x)
f(x) = x² - 8x + 16(x - 4)(x)
f(x) = (x³ - 4x² - 8x² + 32x + 16x - 64)x
f(x) = (x³ - 12x² + 48x - 64)x
f(x) = x⁴ - 12x³ + 48x² - 64x
The equation of the polynomial in standard form is f(x) = x⁴ - 12x³ + 48x² - 64x
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