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name: Mathematics 141 sixth homework due Friday, February 12, 2016 please show your work for full credit 1. Find a linear function with function values f (50) = 0 and f (70) = 2. 2. Use factoring by grouping to determine all the zeroes of x3 + 5x2 − 6x − 30 = 0. 3. Use the difference of squares factoring formula & the quadratic formula to find all solutions of x4 + 4 = 0 (x2 + 2)2 − (2x)2 = 0 4. For the polynomial p(x) = x3 + 6x2 + 14x + 12 it is known that p(−2) = 0 (a) find all the zeroes using long or synthetic division (some zeroes may be complex numbers) (b) write p(x) in completely factored form p(x) = (x − r1 )(x − r2 )(x − r3 ) (c) simplify (p(h) − p(−h))/(2h) (d) sketch a graph of p, showing the correct shape for large |x| and near the x-intercept. 5. Determine the number of solutions each polynomial equation will have: (a) x3 + 6x = 4x − 9x5 (b) (x − 2)3 + 4(x − 2) + 7 5 = x3 + 4x + 7 6. A degree four polynomial with real coefficients has a zero of 4 with multiplicity 2, and has a complex zero of 3 + 2i. Write a formula for the degree four polynomial in factored form.