The factored form of the polynomial function with real coefficients are:
x⁴ - x³ + 2x² - 28x + 24
Given the real coefficients, a lead coefficient of 1, and zeros of − 2 , − 4 , 3 , and 3.
⇒ Zeros: x = -3, -1, 1, 2
⇒ (x + 3)(x + 1)(x - 1)(x - 2)
Multiply the factors.
⇒(x² + 4x + 4)(x - 1)(x - 2)
open the brackets.
⇒ (x² + 4x + 4)(x² - 3x + 2)
⇒ x⁴ + 4x³ + 12x² - 3x³ - 12x² - 36x + 2x² + 8x + 24
Arrange the variables according to the powers.
⇒ x⁴ - x³ + 2x² - 28x + 24
Hence we get the factored form of the polynomial function as:
x⁴ - x³ + 2x² - 28x + 24
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