Final answer:
The statement concerning polynomial solutions is true due to the Rational Root Theorem. The true statements affirm that vectors can form right-angle triangles with their components and that the Pythagorean theorem applies to vectors at right angles. The false statement regarding vector components has been corrected to reflect accurate trigonometric relationships.
Step-by-step explanation:
The statement that "The polynomial may have solutions which are the divisors of -2" is true. According to the Rational Root Theorem, for a polynomial with integer coefficients, any rational solution, when written as a fraction p/q in lowest terms, will have p as a factor of the constant term and q as a factor of the leading coefficient. Since the constant term here is -2, its divisors (which are ±2 and ±1) are potential rational roots of the polynomial.
Regarding the statements about vectors:
- True: A vector can indeed form the shape of a right-angle triangle with its x and y components.
- True: The Pythagorean theorem can be used to calculate the length of the resultant vector when two vectors are at right angles to each other.
- For the last statement, the correct expression should be Ax = A cos 0; Ay = A sin 0. Therefore, it's false that every 2-D vector can be expressed as the product of its x and y-components - it should be expressed as the sum of its components multiplied by the cosine and sine of its angle respective to the axes.