Using the Factor Theorem, the function factored into linear factors is given as follows:
The Factor Theorem states that a polynomial function with roots is given by:
In which a is the leading coefficient.
-9 is a zero of f(x), hence and:
3x³ + 23x² - 35x + 9 = (x + 9)(ax² + bx + c)
ax³ + (b + 9a)x² + (9b + c)x + 9c = 3x³ + 23x² - 35x + 9
The coefficients are given as follows:
- a = 3.
- 9c = 9 -> c = 1.
- b + 9a = 23 -> b = -4.
Hence:
3x³ + 23x² - 35x + 9 = (x + 9)(3x² - 4x + 1)
More can be learned about the Factor Theorem at brainly.com/question/24380382
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