Example 1: Look at the graphs in Fig. 2.9 given below. Each is the graph of y = p(x), where p(x) is a polynomial. For each of the graphs, find the number of zeroes of p(x).
Example 2: Find the zeroes of the quadratic polynomial x2 + 7x + 10, and verify the relationship between the zeroes and the coefficients.
Example 3: Find the zeroes of the polynomial x2 – 3 and verify the relationship between the zeroes and the coefficients.
Example 4: Find a quadratic polynomial, the sum and product of whose zeroes are – 3 and 2, respectively.
Example 5: Verify that 3, –1, −1/3 are the zeroes of the cubic polynomial p(x) = 3x3 – 5x2 – 11x – 3, and then verify the relationship between the zeroes and the coefficients.
Example 6: Divide 2x2 +3x+1 by x+2.
Example 7: Divide 3x3 +x2 +2x+5 by 1+2x+x2.
Example 8: Divide 3x2 – x3 – 3x + 5 by x – 1 – x2, and verify the division algorithm.
Example 9: Find all the zeroes of 2x4 –3x3 –3x2 +6x–2, if you know that two of its zeroes are 2 and − 2.
