Decide whether each of the statements is true or false. provide a counterexample if the answer is false.
a. if a figure has exactly two lines of symmetry, it has exactly two rotational symmetries (including the identity symmetry).
b. if a figure has at least three lines of symmetry, it has at least three rotational symmetries (including the identity symmetry).
c. if a figure has exactly two rotational symmetries (including the identity symmetry), it has exactly two lines of symmetry.
d. if a figure has at least three rotational symmetries (including the identity symmetry), it has at least three lines of symmetry.

Evaluate 8x2 + 9x − 1 2x3 + 3x2 − 2x dx. solution since the degree of the numerator is less than the degree of the denominator, we don't need to divide. we factor the denominator as 2x3 + 3x2 − 2x = x(2x2 + 3x − 2) = x(2x − 1)(x + 2). since the denominator has three distinct linear factors, the partial fraction decomposition of the integrand has the form† 8x2 + 9x − 1 x(2x − 1)(x + 2) = correct: your answer is correct. to determine the values of a, b, and c, we multiply both sides of this equation by the product of the denominators, x(2x − 1)(x + 2), obtaining 8x2 + 9x − 1 = a correct: your answer is correct. (x + 2) + bx(x + 2) + cx(2x − 1).