Use all the skills you have developed in this unit to examine the polynomial f(x)=6x^4−5x^3−9x^2

Question

 a. Use the Remainder Theorem to evaluate f(−2).State your answer in term of f(−2) (SOLVED)

 B. How can the remainder theorem be useful?(SOLVED)

 C. Use the Factor Theorem to completely factor f(x)

 D. Will the factor theorem ever be unsuccessful? Explain why. If so, what will cause it to be unsuccessful?

E. Find all solutions to f(x)=0

I JUST NEED C, D, AND E

Answer 1

C)

f(x) = 6x⁴-5x³-9x² = x²(6x²-5x-9)

Need to concentrate on factoring g(x) = 6x²-5x-9.

Factors of 9 are ±(1,3,9)

Using the factor theorem

g(1) ≠ 0

g(-1) ≠ 0

g(3) ≠ 0

g(-3) ≠ 0

g(9) ≠ 0

g(-9) ≠ 0

Can't be fully factored using the factor theorem

D) Yes. When zeroes are not integers.

E) One factor is x. Use the quadratic equation on g(x) to get the other two roots.