p(x)=2x^3 + 7x^2 + 2x - 3. (a) Use the factor theorem to prove that x + 3 is a factor of p(x). (b) Simplify the expression (2x^3 + 7x^2 + 2x - 3)/(4x^2-1), x!= +- 0.5

(a) The factor theorem states that: the polynomial f(x) has a factor (x - a) if and only if f(a) = 0.Use that information, we know that (x + 3) is a factor of p(x) if p(-3) = 0. So let's test it:p(-3) = 2(-3)^3 +7(-3)^2 +2(-3) - 3 = 2(-27) + 7(9) -6 -3 = -54 + 63 -9 = 0.(b) Notice here that the numerator is just p(x) and that the denominator is just (2x + 1)(2x - 1).Since we know that (x + 3) is a factor is p(x), we can factorise it out of our polynomial:2x^3 + 7x^2 + 2x - 3 = (x + 3)(2x^2 + x - 1) = (x + 3)(2x - 1)(x + 1)So putting all this information into our expression gives us:(x + 3)(2x - 1)(x + 1)/(2x + 1)(2x - 1) Cancel out the (2x - 1) term.(x + 3)(x + 1)/(2x + 1)