Question

ALGEBRA 2 HELP!!! Find all the linear factors f(x)=2%7D%20%20%20%2B28x-8" id="TexFormula1" title="3x^{4}-7x^{3}-10x^{2} +28x-8" alt="3x^{4}-7x^{3}-10x^{2} +28x-8" align="absmiddle" class="latex-formula">

Answer 1

Answer:

x + 2

3x − 1

x − 2

Step-by-step explanation:

The order of the polynomial is 4, so there are 4 roots.

Use rational root theorem to find possible rational roots.

±1, ±2, ±4, ±8, ±1/3, ±2/3, ±4/3, ±8/3

By trial and error, -2, ⅓, and 2 are all roots.  The fourth root can't be imaginary (complex roots come in pairs), so one of the real roots must be repeated.

Answer 2

Answer: the factors are (x - 2)(x + 2)(3x - 1)

Step-by-step explanation:

The given polynomial function is expressed as

f(x) = 3x⁴ - 7x³ - 10x² + 28x - 8

The first step is to test for any value of x that satisfies the polynomial when

3x⁴ - 7x³ - 10x² + 28x - 8 = 0

Assuming x = 2, then

3(2)⁴ - 7(2)³ - 10(2)² + 28 × 2 - 8 = 0

48 - 56 - 40 + 56 - 8 = 0

0 = 0

It means that x - 2 is a factor.

To determine the other factors, we would apply the long division method. The steps are shown in the attached photo. Looking at the photo, we would factorize the quadratic equation which is expressed as

3x² + 5x - 2 = 0

3x² + 6x - x - 2 = 0

3x(x + 2) - 1(x + 2)

(3x - 1)(x + 2) = 0