Hi Mike! In SAT official test 1, Q 29 (in the math calculator section), how do you solve this problem?

Hi Mike! In SAT official test 1, Q 29 (in the math calculator section), how do you solve this problem? I don’t quite understand the explanation/concepts mentioned in the book.

29)For a polynomial p(x), the value of p(3) is -2. Which of the following must be true about p(x)?

A) x-5 is a factor of p(x).
B) x-2 is a factor of p(x).
C) x+2 is a factor of p(x).
D) The remainder when p(x) is divided by x-3 is -2.

(Also what does PWN stand for?)

This may be a little advanced for the SAT…

This may be a little advanced for the SAT, but complex numbers sometimes show up –as do cubic polynomials– so hopefully you can address this for me! TIA!

Which of the following could be the full set of complex roots of a cubic polynomial with real coefficients?

A. { 0, 1, i}
B. {1, i, 2i}
C. {2, i}
D. {3, 2 + i, 2 – i}

Would you please show an easy way to solve this…?

Would you please show an easy way to solve this:

a(x) = x^3 +3x^2 + 5x
b(x) = 5x^2 + 17x + 16

Polynomial a(x) and b(x) are defined above. Which of the polynomials below has a factor of 3x + 2 ?

(A) l(x) = a(x)+ b(x)
(B) m(x) = 3a(x) + b(x)
(C) n(x) = a(x) – 3b(x)
(D) p(x) = 2a(x) + 3b(x)