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torisob [31]
2 years ago
11

Factor ​f(x) =3x^2+23x^2-35x+9 into linear factors given that -9 is a zero of​ f(x).

Mathematics
1 answer:
Evgesh-ka [11]2 years ago
6 0

Using the Factor Theorem, the function factored into linear factors is given as follows:

3x^2 + 23x^2 - 35x + 9 = 3(x + 9)(x - 1)\left(x - \frac{1}{3}\right)

<h3>What is the Factor Theorem?</h3>

The Factor Theorem states that a polynomial function with roots x_1, x_2, \codts, x_n is given by:

f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)

In which a is the leading coefficient.

-9 is a zero of f(x), hence x_1 = -9 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)

3x^2 + 23x^2 - 35x + 9 = 3(x + 9)(x - 1)\left(x - \frac{1}{3}\right)

More can be learned about the Factor Theorem at brainly.com/question/24380382

#SPJ1

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