  • Matrices
• Algebra
• Geometry
• Funciones
• Trigonometry
• Coordinate geometry
• Combinatorics
 Suma y resta Producto por escalar Producto Inversa
 Monomials Polynomials Special products Equations Quadratic equations Radical expressions Systems of equations Sequences and series Inner product Exponential equations Matrices Determinants Inverse of a matrix Logarithmic equations Systems of 3 variables equations
 2-D Shapes Areas Pythagorean Theorem Distances
 Graphs Definition of slope Positive or negative slope Determine slope of a line Ecuación de una recta Equation of a line (from graph) Quadratic function Posición relativa de dos rectas Asymptotes Limits Distancias Continuity and discontinuities
 Sine Cosine Tangent Cosecant Secant Cotangent Trigonometric identities Law of cosines Law of sines
 Ecuación de una recta Posición relativa de dos rectas Distancias Angles in space Inner product

 Polynomials Remainder theorem Remainder theorem. If p(x) is divides by (x-c) the remainder is a constant and and is equal to p(c) Supose that we divide the polynomial P(x)=2x3-5x+3 by x=1. Then according to the remainder theorem, the remainder in this case should be the number p(1). Let's check: The remainder is 0 and P(1) = 0. As the calculations show, the remainder is indeed equal to p(1) Use the remainder theorem to find the remainder when P(x)=2x3-5x+3 is divided by x-1. P(1)=2·13-5·1+3=2-5+3=0. Thus the remainder is 0. Proof of the remainder theorem To prove the remainder theorem we must show that when the polynomial P(x) is divided by x-a, the remainder is P(a). Now, according to the division algorithm, we can write P(x)=(x-a)·q(x) + r(x) (1) for unique polynomials q(x) and r(x). In this identity, either r(x) is the zero polynomial or the degree of r(x) is less than that of x-a. Since the degree of x-a is 1, the degree of r(x) must be zero. Thus in either case, the remainder r(x) is a constant. Denoting this constant by r, we can rewrite equation (1) as:P(x)=(x-a)·C(x) + r. If we set x=a in this identity we obtain P(a)=(a-a)·C(a) + r =r . We have now shown that P(a) = r. But by definition, r is the remainder r(x). Thus P(a) is the remainder. This proves the remainder theorem. Use the remainder theorem to evaluate the polynomial when Solution: