Consider two polynomials A(x) and B(x).
a. (i) Explain, in your own words, why the sign of every term in B(x) must be changed when subtracting B(x) from A(x). Give a brief reason based on basic algebraic properties.
b. (ii) Using A(x)=3x2−4x+7 and B(x)=−2x2+5x−3, find and simplify A(x)−B(x).
c. (iii) State the degree of the simplified polynomial obtained in part (ii) and briefly justify how combining like terms determines this degree.