Textbook QuestionDetermine whether each statement is true or false. If false, explain why. Because x-1 is a factor of ƒ(x)=x^6-x^4+2x^2-2, we can also conclude that ƒ(1)=0190views
Textbook QuestionIn Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. f(x)=3x^4−11x^3−x^2+19x+6187views
Textbook QuestionUse the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. See Example 1. x^3-5x^2+3x+1; x-1139views
Textbook QuestionIn Exercises 9–16, a) List all possible rational zeros. b) Use synthetic division to test the possible rational zeros and find an actual zero. c) Use the quotient from part (b) to find the remaining zeros of the polynomial function. f(x)=2x^3−3x^2−11x+6180views
Textbook QuestionIn Exercises 25–32, find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value. n=3; 1 and 5i are zeros; f(-1) = -104368views
Textbook QuestionShow that each polynomial function has a real zero as described in parts (a) and (b). In Exercises 31 and 32, also work part (c). ƒ(x)=4x^3-37x^2+50x+60 Find the zero in part (b) to three decimal places.152views
Textbook QuestionFactor ƒ(x) into linear factors given that k is a zero. See Example 2. ƒ(x)=2x^4+x^3-9x^2-13x-5; k=-1 (multiplicity 3)187views
Textbook QuestionShow that each polynomial function has a real zero as described in parts (a) and (b). In Exercises 31 and 32, also work part (c). ƒ(x)=6x^4+13x^3-11x^2-3x+5 no zero greater than 1211views
Textbook QuestionIn Exercises 39–52, find all zeros of the polynomial function or solve the given polynomial equation. Use the Rational Zero Theorem, Descartes's Rule of Signs, and possibly the graph of the polynomial function shown by a graphing utility as an aid in obtaining the first zero or the first root. f(x)=x^3−4x^2−7x+10307views
Textbook QuestionIn Exercises 47–48, find an nth-degree polynomial function with real coefficients satisfying the given conditions. Verify the real zeros and the given function value. n = 3; 2 and 2 - 3i are zeros; f(1) = -10807views
Textbook QuestionFor each polynomial function, find all zeros and their multiplicities. ƒ(x)=(x+1)^2(x-1)^3(x^2-10)160views
Textbook QuestionFind a polynomial function ƒ(x) of degree 3 with real coefficients that satisfies the given conditions. See Example 4. Zeros of -2, 1, and 0; ƒ(-1)=-1212views
Textbook QuestionFind a polynomial function ƒ(x) of degree 3 with real coefficients that satisfies the given conditions. See Example 4. Zero of -3 having multiplicity 3; ƒ(3)=36285views
Textbook QuestionDetermine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=4x^3-x^2+2x-7162views
Textbook QuestionDetermine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=6x^4+2x^3+9x^2+x+5165views
Textbook QuestionDetermine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=5x^6-6x^5+7x^3-4x^2+x+2162views
Textbook QuestionFind all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.* ƒ(x)=x^4+x^3-9x^2+11x-4204views