Using the Factor Theorem, the function factored into linear factors is given as follows:
[tex]3x^2 + 23x^2 - 35x + 9 = 3(x + 9)(x - 1)\left(x - \frac{1}{3}\right)[/tex]
The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
-9 is a zero of f(x), hence [tex]x_1 = -9[/tex] 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:
Hence:
3x³ + 23x² - 35x + 9 = (x + 9)(3x² - 4x + 1)
[tex]3x^2 + 23x^2 - 35x + 9 = 3(x + 9)(x - 1)\left(x - \frac{1}{3}\right)[/tex]
More can be learned about the Factor Theorem at https://brainly.com/question/24380382
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