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2 years ago

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

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Exercise 1: The length of the unknown leg is 4 inches.

Exercise 3: The following straws can be used to construct the triangle: b) $3\,in$ , c) $4.5\,in$ , d) $6.5\,in$ , e) $10\,in$ , f) $13.5\,in$

Exercise 4: Possible options of this exercise: 1) (2, 4, 5), 2) (4, 5, 6), 3) (5, 6, 10), 4) (1, 2, 11), 5) (1, 4, 11), 6) (1, 10, 11)

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Let suppose that triangle represented in the figure is a right triangle, the length of the missing leg is determined by Pythagorean Theorem:

$y = \sqrt{l^{2}-x^{2}}$ (1)

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$l$ - Hypotenuse, in inches.

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$14\,in > l > 2\,in$

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