Matching In Exercises 5-8, match the rational expression with the form of its decomposition. [The decompositions are labeled (a), (b), (c), and (d).]
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- Using Technology In Exercises 9 and 10, (a) use a graphing utility to graph the two equations in the same viewing window, (b) use the graphs to verify that the expressions are equivalent, and (c) use long division to verify the results algebraically. y1=x2+2x1x+3,y2=x1+2x+3arrow_forwardIn Exercises 2-6, fill in the blanks. The Theorem states that if a polynomial f(x)is divided by xk,then the remainder is r=f(k).arrow_forwardIn Exercises 2-6, fill in the blanks. A shortcut for long division of polynomials is ,in which the divisor must be of the form xk.arrow_forward
- Using the Remainder Theorem In Exercises 51-54, use the Remainder Theorem and synthetic division to find each function value. Verify your answers using another method. h(x)=x35x27x+4(a)h(3)(b)h(12)(c)h(2)(d)h(5)arrow_forwardApproximating 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_forwardmax.: ssegna cedente The polynomial x4 + 3x³8x24 is divisible with O (A) (x - 2) O (B) (x - 1) O (C) (x-2)(x - 1) O (D)(x - 2)² O (E) (x + 1)² Successivo CELE ASSESMEN ndf Ma 09.arrow_forward
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- List all zeros and their multiplicities, degree, end behavior, and behavior of the graph at the zero. a) f(x) = -2x(x-2)(x + 1)² b) g(x) = x5 - 3x4- x3 + 11x2 - 12x + 4 12) What are the two types of polynomial division and what are the advantages and disadvantages of each. %3D %3Darrow_forwardIn Exercises 2-6, fill in the blanks. In the Division Algorithm, the rational expression r(x)/d(x)is because the degree of r(x)is less than the degree of d(x).arrow_forward
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