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bat Reader File Edit View Window Help MATH107Sp2018Katiraie pd Tools MATH107Sp2018 * College Algebra MATH 107 Spring, 2018, V1.2 20. Consider the polynomial Px), shown in both standard form and factored form. P(x)=1x" +1x'-7x2-1x+2=1(x + 3)(x + 1)(x-1)(x-2) (a) Which sketch illustrates the end behavior of the polynomial function? A. B. C. D. Answer: (b) State the zeros of the function. (e) State the -intercept (d) State which graph below is the graph of Pa). GRAPH A Answer Answer: Answer: GRAPH B

Explanation / Answer

(a) By observing the equation, we see that x4 will be the dominant factor when x increases both in positive and negative direction and P(x) will increase exponentially for larger values of x. Since x4 is positive for both positive and negative values of x.

So option C is correct about the end-shape of the polynomial.

(b) Since the polynomial is expressed in factor form, the zeros occur at x= -3, -1, 1 and 2.

(c) The y-intercept can be found by putting x=0 in the equation. Then P(x) = 2.

So the y-intercept is 2.

(d) The polynomial increases exponentially for large values of x. So from the 4 options provided, either (B) or (C) are correct.

We also know that the y-intercept is 2. This is true for the graph in option B.

So Graph B is the correct option.

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