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Factorization

Definitions and notations

Math

Definitions:

  • Factors: Let p(x)p(x), q(x) and r(x) be three polynomials such that, p(x)×q(x)=r(x),p(x)\times q(x)= r(x), then p(x)p(x) and q(x)q(x) are said to be the factors of r(x)r(x).

  • Remainder Theorem: When a polynomial of degree n1n\ge 1 is divided by (xa)(x-a), then the remainder RR is found by R=p(a)R = p(a).

  • Zero of a polynomial: Let p(x)=a0+a1x+a2x2++anxnp(x) = a_0 + a_1x + a_2x^2 + \dots + a_nx^n be a polynomial with real coefficients. By putting x=ax = a in the polynomial p(x)p(x), if p(a)p(a) equals zero then, i.e. p(a)=0p(a) = 0, then a“a” is said to be a zero of the polynomial p(x)p(x).

  • Synthetic Division: Synthetic Division is a method of dividing a polynomial with a linear factor.

  • Cubic Polynomial: A polynomial of order three (3) is called a cubic polynomial.