Question

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

Answer 1

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

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

What is the Factor Theorem?

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