The number of for which the system of linear equations has no solution, is (A) 6 (B) 7 (C) 8 (D) 9 Solution: Tip for solving this question: By converting linear equations into matrix form, find the determinant of the matrix. Also, check out What is Determinant of Matrix in detail here. Then using properties […]

## Division of Polynomial Fractions

Division of polynomial fraction is same as multiplication, the difference is that we have to flip the fraction which appears after the division sign and change it into multiplication sign and then simplify. Remember it is essential to change the fraction and multiply thereafter to cancel it further.

## Multiplying polynomial fractions

Multiplication of polynomial fraction is same as the arithmetic fraction but the difference is to factor the numerator and denominator completely and then reduce it or canceling out the common factors of both the numerator and denominator and then multiply the remaining fraction.

## Subtraction of Polynomial Fractions

Subtraction of polynomial fractions with common denominators and if not we have to find the LCD [Least common denominator] and by multiplying the numerators as well as the denominator of each expression by any factors which make it equal to the LCD and simplify the numerator by factoring it, if possible.

## Addition of Polynomial Fractions

Addition of polynomial fractions with common denominators and if not we have to find the LCD [Least common denominator] and by multiplying the numerators as well as the denominator of each expression by any factors which make it equal to the LCD and simplify the numerator by factoring it, if possible.

## Roots of a Polynomial

A polynomial is defined as the sum of more than one or more algebraic terms where each term consists of several degrees of same variables and integer coefficient to that variables. x2−3×2−3, 5×4−3×2+x−45×4−3×2+x−4 are some examples of polynomials. The roots or also called as zeroes of a polynomial P(x) for the value of x for […]

## Simplifying Polynomial Fractions

Polynomial Fraction is an expression of the ratio of two polynomials. Fractions with polynomials in the numerator and/or denominator can often be simplified by factoring and reducing to lowest terms.

## Factor Theorem of Polynomial

Polynomial is an expression of the form: . Where n is a natural number and . There are 2 theorems which play a vital role in solving polynomial which is remainder theorem and factor theorem. Factor theorem is being derived from the remainder theorem which allows us to initially study remainder theorem first then the factor theorem. According to […]

## Remainder Theorem of Polynomials

Remainder Theorem: If a polynomial f(x) is divided by x-r, the remainder is equal to the value of the polynomial where r is substituted for x. Divide the polynomial by x-r until the remainder, which may be zero is independent of x. Denote the quotient by Q(x) and the remainder by R. Then according to the meaning of the division, f(x) = (x-r) Q(x) + R.

## Zeroes of Polynomial

Zeros of the polynomial with its functions and how to solve the real and complex of zeros of the polynomial.

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