Jse the remainder theorem to find P (2) for P (x)=x-4x-4x+9. Specifically, give the quotient and the remainder for the associated division and the value of P (2). Quotient = Remainder = P(2) = 0

Using Descartes’ Rule of Signs. we can tell that the polynomial P(x)=x53x4+x2+8x8 has _______________, ____________________positive real zeros and _____________negative real zeros.

Remainder Theorem Use synthetic division and the Remainder Theorem to evaluate P(c) . P(x)=2x6+7X5+40x47x2+10x+112,c=3

DISCOVER: Nested Form of a Polynomial Expand Q to prove that the polynomials P and Q are the same. P(x)=3x45x3+x23x+5 Q(x)=(((3x5)x+1)x3)x+5 Try to evaluate P(2) and Q(2) in your head, using the forms given. Which is easier? Now write the polynomial R(x)=x52x4+3x32x2+3x+4 in nested form, like the polynomial Q. Use the nested form to find R(3) in your head. Do you see how calculating with the nested form follows the same arithmetic steps as calculating the value of a polynomial using synthetic division?