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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.