Question

One factor of f (x ) = 5 x cubed 5 x squared minus 170 x 280 is (x 7). What are all the roots of the function? Use the Remainder Theorem. X = –4, x = –2, or x = 7 x = –7, x = 2, or x = 4 x = –7, x = 5, or x = 280 x = –280, x = –5, or x = 7.

Answer 1

To solve the problem we must know about the Remainder Theorem.

What is the Remainder theorem?

According to the remainder theorem, when a polynomial P(x) is divided by (x-t) then the remainder of the division is equal to P(t). If P(t)=0, then the (x-t) is the factor of the polynomial.

The roots of the function are -7, 2, and 4.

Given to us

• One factor of f (x) = $5x^3+5x^2-170x+280$ is (x +7).

What is the quotient of the function?

We know (x+7) is the factor of the function, f(x) = $5x^3+5x^2-170x+280$,

therefore,

$f(x) =5x^3+5x^2-170x+280 = [(x+7) \times quotient] + Remainder$

As (x-2) is the factor of the function, therefore, the remainder will be zero for the equation,

$\rm quotient=\dfrac{5x^3+5x^2-170x+280}{(x+7)}$

$\rm quotient=5x^2-30x+40$

What are the factors of the function?

Solving the quadratic equation,

$5x^2-30x+40\\\text{Dividing the equation by 5}\\\\=x^2-6x+8\\=(x-2)(x-4)$

Hence, the roots of the function are -7, 2, and 4.

Learn more about Remainder theorem:

https://brainly.com/question/4515216

Answer 2

Answer:

its b

Step-by-step explanation: