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

$x\text{ = }-\frac{1}{2}$

or

$x\text{ = }\frac{1}{2}$

then, the zeros (roots or solutions) are:

$x\text{ }=\text{ 3, x = -}\frac{1}{2},\text{ x = }\frac{1}{2}$

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:

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