Points to Remember

Algebra

Points to Remember

• An algebraic expression of the form p ( x) = a_n xⁿ + a_n − ₁ x^n-1 + ... + a₂ x² + a₁x + a₀ is called Polynomial in one variable x of degree ‘n’ where a₀, a₁, a₂, ...a_n are constants (a_n ≠ 0) and n is a whole number.

• Let p(x) be a polynominal. If p(a) = 0 then we say that ‘a’ is a zero of the polynomial p(x)

• If x = a statisfies the polynominal p(x) = 0 then x = a is called a root of the polynominal equation p(x) = 0.

• Remainder Theorem: If a polynomial p(x) of degree greater than or equal to one is divided by a linear polynomial (x–a), then the remainder is p(a), where a is any real number.

• Factor Theorem

If p(x) is divided by (x -a) and the remainder p(a ) = 0, then (x -a) is a factor of the polynomial p(x)

• Solution of an equation is the set of all values that when substituted for unknowns make an equation true.

• An equation with two variable each with exponent as 1 and not multiplied with each other is called a linear equation with two variables.

• Linear equation in two variables has infinite number of solutions.

• The graph of a linear equation in two variables is a straight line.

• Simultaneous linear equations consists of two or more linear equations with the same variables.