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Social ScienceQuestion 4:Consider the polynomial equation8x44318a211- 2 =0(a) Using the Rational Root Theorem, show work to find the possible roots c of this equation(b) Using synthetic division, show work to find one rational root c. Hint: try positive c's.(c) Use the Factor Theorem to rewrite f as f (x) = (x - c)q(x) with the synthetic division you just did.(d) Using the Rational Root Theorem for q(x), show work to find possible zeros c of q(e) Using synthetic division, show work to find one rational root c2 of q. Hint: try positive c's.(f) Use the Factor Theorem to write q(x) = (x - c2)q2(x) with the new root c2 and new quotient q2.(This is two problems in oneit will be separated for test purposes, with different numbers, of course)
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Question 4: Consider the polynomial equation 8x443 18a211- 2 = 0 (a) Using the Rational Root Theorem, show work to find the possible roots c of this equation (b) Using synthetic division, show work to find one rational root c. Hint: try positive c's. (c) Use the Factor Theorem to rewrite f as f (x) = (x - c)q(x) with the synthetic division you just did. (d) Using the Rational Root Theorem for q(x), show work to find possible zeros c of q (e) Using synthetic division, show work to find one rational root c2 of q. Hint: try positive c's. (f) Use the Factor Theorem to write q(x) = (x - c2)q2(x) with the new root c2 and new quotient q2. (This is two problems in one it will be separated for test purposes, with different numbers, of course)
Expert Answer
Given that the polynomial
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8x4x3-18x2 +11x-2 = 0
- Find out the factors using rational root theorem
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According to the rational root theorem n-1 ..axc then every rational root of f(x) If the polynomial f(x)= a,x" +a^x' р has form of where p is a factor of constant "c" and q is a factor of leading coefficient a, а
Here the constant is -2 and le...
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The factors of -2 1±2 And the factor of leading coefficient 8 =±1±2±4±8 Possible roots of the f(x) 1 2 1 2 1 2 1 2 1 1 1 tl,,24 8
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