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Finding a Polynomial
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- Sketching the Graph of a Polynomial Function In Exercises 71-84, sketch the graph of the function by (a) applying the Leading Coefficient Test, (b) finding the real zeros of the polynomial, (c) plotting sufficient solution points, and (d) drawing a continuous curve through the points. f(x)=3x315x2+18xarrow_forwardFinding a Polynomial Function In Exercises 53-62, find a polynomial function that has the given zeros. (There are many correct answers.) 2,5arrow_forwardFinding Real Zeros of a Polynomial Function In Exercises 33-48, (a) find all real zeros of the polynomial function, (b) determine whether the multiplicity of each zero is even or odd, (c) determine the maximum possible number of turning points of the graph of the function, and (d) use a graphing utility to graph the function and verify your answers. f(t)=2t42t240arrow_forward
- Approximating Zeros In Exercises 71-76, (a) use the zero or root feature of a graphing utility to approximate the zeros of the function accurate to three decimal places, (b) determine the exact value of one of the zeros, and (c) use synthetic division to verify your result from part (b), and then factor the polynomial completely. h(t)=t32t27t+2arrow_forwardApplying the Leading Coefficient Test In Exercises 19-28, describe the left-hand and right-hand behavior of the graph of the polynomial function. f(x)=12x3+4xarrow_forwardFill in the blanks. The Theorem states that if fis a polynomial function such thatf(a)f(b),then, in the interval [a,b],ftakes on every value between f(a)and f(b)arrow_forward
- True or False? In Exercises 99-102, determine whether the statement is true or false. Justify your answer. If f is a polynomial function of x such that f(2)=6andf(6)=6, then f has at most one real zero between x=2andx=6.arrow_forwardFill in the blanks. When a real zero xa of a polynomial functionfis of even multiplicity, the graph of fthe x-axisatx=a,and when it is of odd multiplicity, the graph of f the x-axisatx=a.arrow_forwardFill in the blanks. When x=a is a zero of a polynomial function f, the three statements below are true. (a) x=ais a of the polynomial equation f(x)=0. (b) is a factor of the polynomial f(x). (c) (a,0)is an of the graph of f.arrow_forward
- Finding the Zeros of a Polynomial Function In Exercises 49-58, use the given zero to find all the zeros of the function. FunctionZerofx=x3x2+4x42iarrow_forwardFill in the blanks. A polynomial function is written in form when its terms are written in descending order of exponents from left to right.arrow_forwardFinding the Zeros of a Polynomial Function In Exercises 73-78, find all the zeros of the function. When there is an extended list of possible rational zeros, use a graphing utility to graph the function in order to disregard any of the possible rational zeros that are obviously not zeros of the function. fs=2s35s2+12s5arrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning