1. Find all zeros of the polynomial P(x) = 3x 4 + 26 x 3 + 74 x 2 + 74 x + 15 knowing that P(x) has two rational zeros.

2. Polynomial P(x) = x 3 + x 2 + c x + d has x – 2 as a factor and when divided by x – 1, the remainder is equal to 3. Find the constant c and d.

3. P(x) is an even fourth degree polynomial function such that P(-2) = 0, P(x + 3) has a zero at x = 4 and P(0) = -9. Find P(x).

4. The polynomial P(x) = 2 x 4 + 3 x 3 – 16 x 2 – 17 x + 12 has zeros at x = 1/2 and x = -3. Find the other zeros.

5. Factor the following polynomials:

a) f(x) = x 3 – x 2 – 4 x + 4

b) f(x) = 2 x 2 – x 3

c) f(x) = x 2 – 2 x 4

d) f(x) = -(x 2 – 2 x – 3) 2

e) f(x) = x 4 + 3 x 3 + 3 x 2 + x

10. A polynomial of degree 4 has a negative leading coefficient and simple zeros (i.e. zeros of multiplicity 1) at x = 2, x = -2, x = 1 and x = – 1. Is the y intercept below the x axis or above the x axis?

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