Question

I need help with part C and D from question 6

Answer 1

Question: part C and D:

Solution:

C) Find the remaining zeros of f(x):

Let the following polynomial function:

`f(x)=8x^4-20x^3-14x^2+5x+3`

Remember that the roots or zeros are the y-intersections of the function, that is when y=0. Now, to find the zeros of this function we must factor the following expression:

`8x^4-20x^3-14x^2+5x+3=0`

the factor of this expression is:

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

now, applying the zero factor theorem, we get the following:

`x-3\text{ = 0}`

or

`2x+1=0`

or

`2x-1=0`

solving for each one of the above equations we get:

`x\text{ = }3`

or

`x\text{ = }-(1)/(2)`

or

`x\text{ = }(1)/(2)`

then, the zeros (roots or solutions) are:

`x\text{ }=\text{ 3, x = -}(1)/(2),\text{ x = }(1)/(2)`

D) write the complete linear factorization of f(x)

According to the above results, we get that the complete linear factorization of f(x) is:

`f(x)=(x-3)(2x+1)(2x+1)^{}(2x-1)`