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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College Algebra
- In 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_forwardUsing 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. A shortcut for long division of polynomials is ,in which the divisor must be of the form xk.arrow_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_forwardUsing 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_forwardLet P(x) = 2x - 9x2 - 6x +5 (a) List all possible rational zeros of P. (Enter your answers as a comma-separated list.) (b) Find the complete factorization of P. (c) Find the zeros of P. (Enter your answers as a comma-separated list. Enter all answers including repetitions.) (d) Sketch the graph of P. 100 100t 50 50 -6 -2 6 -6 -4 -2 -50 -50 100 100 y y 100 100- 50 50 -4 -2 2 4 6. -6 -4 -2 2 -50 -50 100F 100arrow_forward
- Let P(x) = 2x3 - 5x2 - 4x + 3. (a) List all possible rational zeros of P. (Enter your answers as a comma-separated list.) la (b) Find the complete factorization of P. (c) Find the zeros of P. (Enter your answers as a comma-separated list. Enter all answers including repetitions.) (d) Sketch the graph of P. y y 30 30 20 20 10 10 -6 -4 -2 2 4 6. -6 -4 -2 2 4 6 -10 -10 -20 - 20 -30 -30 y y 30 30 20 20 10 10 -6 -4 -2 2 4 6 -6 -4 -2 2 4 -10- -10- -20 -20 30 -30arrow_forwardLet P(x) = 2x3 – 5x? - 4x + 3. %3D (a) List all possible rational zeros of P. (b) Find the complete factorization of P. (c) Find the zeros of P. (d) Sketch the graph of P.arrow_forwardConsider the division of two polynomials: f(x) - (x-c). The result of the synthetic division process is shown here. Write the polynomials representing the (a) Dividend, (b) Divisor, (c) Quotient, and (d) Remainder. -2 ] 1 4 8 8 -2 -4 -8 1 2 4 Part: 0/ 4 Part 1 of 4 (a) The dividend isarrow_forward
- Consider the division of two polynomials: f(x)+(x-c). The result of the synthetic division process is shown here. Write the polynomials Dividend, (b) Divisor, (c) Quotient, and (d) Remainder. 3 2 -7 6 8 9 -12-12 2 -1 -4 -4 -3 Part: 0/4 Part 1 of 4 (a) The dividend is Xarrow_forwardLet P(x) 2x3 – 9x2 – 6x + 5. (a) List all possible rational zeros of P. (Enter your answers as a comma-separated list.) (b) Find the complete factorization of P. (c) Find the zeros of P. (Enter your answers as a comma-separated list. Enter all answers including repetitions.) (d) Sketch the graph of P. y y 100 100- 50 50 WebAssign Plot 4 -6 -4 -2 6 -6 6 -50 =50 100 -100 y 100- 100- 50 50 -6 -4 -2 2. 4 6 -6 -4 -2 2 -50 =50 100- 100-arrow_forwardPartial fraction decomposition involves finding a single rational expression for a given sum or difference of rational expressions. Determine whether the statement makes sense or does not make sense, and explain your reasoningarrow_forward
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