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# Points to Remember

Maths : Algebra : Points to Remember

Algebra

Points to Remember

An algebraic expression of the form p ( x) = an xn + an1 xn-1 + ... + a2 x2 + a1x + a0 is called Polynomial in one variable x of degree ‘n’ where a0, a1, a2, ...an are constants (an ≠ 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 (xa), 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.

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