please help me to understand the work that I need to assist my daughter on

Explain how to use the Factor Theorem and what information the theorem tells us. Use the Factor Theorem to determine whether the given smaller polynomial is a factor of the larger polynomial: a} (x+1); P(x)=2x"+2x3x25x4 b] (xZ): P(X)=5x3x27 Factor each expression using the Factor by Grouping method or the Sum; Difference of Two Perfect Squares or Cubes method (whichever is appropriate for a given problem): a} X3+ 5x24x20 b) x3 + 64 6) Elm2 - 64 d) 26 an e) 4x3+8x2+2x+4 f} Y3 125 Factor the equation 81x\" 10000 Show how to determine whether {2x 4) is a factor of the polynomial 2x5 4x\" + 2X2 2x 4