# Functions

Please help me with the attached problems by explaining how to solve them.

Use synthetic division to divide the polynomial 4x3 + 10x2 - 11 by x + 3, and state the quotient polynomial and the remainder. [Be careful - notice that there is no x term.]. Show work.

Consider the polynomial f(x) = 5x3 - 9x2 - 17x - 3.

(a) By using the Rational Zero Theorem, list all possible rational zeros of the given polynomial.

(b) Find all of the zeros of the given polynomial. Be sure to show work, explaining how you have found the zeros.

Let .

(a) Find the domain.

(b) Determine the vertical asymptote(s).

(c) Determine the horizontal asymptote or oblique asymptote.

(d) Find the y-intercept.

(e) Find the x-intercept(s).

House of Representative. The number of representative N that each state has varies directly as the number of people P living in the state. If NY with 19,227,088 residents has 29 representatives, how many representatives does NC with a population of 8,541,222 have?

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

Please see the attachment for full solution.

Problem #1

By the synthetic division algorithm we have the followings

So the quotient polynomial is and the remainder is .

Problem #2

(a) According to the Rational Zero Theorem, all possible zeros of the polynomials are

(b) We need to try the above possible zeros in the polynomial and find which one makes the polynomial zero. We get

Then by factorization, we get

Therefore, the other two zeros are .

Thus all zeros are .

Problem #3

(a) The domain of the function is all real numbers except .

(b) The vertical asymptotes are and .

(c) The horizontal asymptote is .

(d) Since , then the y-intercept is .

(e) Let , then . Thus the x-intercepts are .

Problem #4

Suppose NC has representatives, then we have

So NC should have 13 representatives.

Â© BrainMass Inc. brainmass.com October 5, 2022, 6:03 pm ad1c9bdddf>https://brainmass.com/math/basic-algebra/synthetic-division-rational-zero-theorem-domain-asymptotes-240853