f(x) = x³ + 2x² - 15x - 36 is the equation of a degree 3 polynomial (in factored form) with the given zeros of f(x) are − 3 , 4 , − 3 assuming that the leading coefficient is 1. This can be obtained by formula of polynomial function.
<h3>Find the required equation:</h3>
- The zeroes or roots of a polynomial function are x values for which f(x) = 0
- If the zeroes or roots are r₁, r₂, r₃,... then possible polynomial function is
⇒ f(x) = a(x - r₁)(x - r₂)(x - r₃)
where a is the leading coefficient
Here in the question it is given that,
- Polynomial should be with degree 3
- zeros of f(x) are − 3 , 4 , − 3
By using the formula of polynomial function we get,
⇒ f(x) = a(x - r₁)(x - r₂)(x - r₃)
⇒ f(x) = 1(x - (-3))(x - (4))(x - (-3))
⇒ f(x) = 1(x + 3)(x - 4)(x + 3)
⇒ f(x) = (x + 3)(x² - x - 12)
⇒ f(x) = x³ - x² - 12x + 3x² - 3x - 36
⇒ f(x) = x³ + 2x² - 15x - 36
Hence f(x) = x³ + 2x² - 15x - 36 is the equation of a degree 3 polynomial (in factored form) with the given zeros of f(x): − 3 , 4 , − 3 assuming that the leading coefficient is 1.
Learn more about polynomial function here:
brainly.com/question/12976257
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