Remainder Theorem Learn about Remainder theorem concept. When we divide a number by another number, we get a quotient and a remainder. If remainder is zero then we say the numerator is divisible by denominator. The same concept is used here in polynomials. When a polynomial is divided by another polynomial we get a quotient polynomial and a remainder in specific. If f (x) is a polynomial, When f (x) is divided by (x-a) the remainder is f (a) and if the remainder f (a) = 0 then (x - a) is a factor of the expression f (x).Conversely, for the expression f (x), if f (a) =0, then (x-a) is a factor and (a) is a root. Steps for Factorization Using Remainder Theorem By trial and error method, find the factor of the constant for which the given expression becomes equal to zero. Divide the expression by the factor that is determined in step 1. Know More About Solving Multistep Equations
Factorize the quotient. If the quotient is a trinomial, factorize it further. If the expression is a 4th degree expression, the first step will be to reduce this to a trinomial and then factorize this trinomial further. Remainder Theorem Examples Below are the examples on remainder theorem Example 1: Find the remainder when 2x3+4 is divided by a) x-1 b) x-2 c) x+1 Solution : Let f(x) = 2x3 + 4 a) When f (x) is divided by x-1, R = f (1) = 2(1)3+ 4 =6 Learn More About What is a Function in Algebra
b) When f (x) is divided by x-2, R = f (2) = 2(2)3+ 4 = 20 c) When f(x) is divided by x+1, i.e., x-(-1). R = f(-1) = 2(-1)3 + 4 = -2+4 = 2 Example 2: Factorize x2 - 7x + 10. Solution: Let f(x) = x2 - 7x + 10 Then f (2) = (2)2 - 7(2) +10 [By trial and error method] = 4 - 14 + 10 = 0
What is a Polynomial General representation of polynomial: F(x) = an Xn + an-1Xn-1 + an-2Xn-1……………. + a1X + a0 Where n= positive number a=real numbers The highest value of exponents is called degree of polynomial. a0, a1, a2… are called as co-efficient. Let us see internet solving polynomials in this article. What is Polynomial Polynomial :- The form of an monomial is expression is a(xn) where n is non-negative integer. The variable ‘a’ is called as coefficient of xn and n is the degree of the monomial. Based on the n value monomial is called as monomial (when n=1), two
degree polynomial (when n=2) and three degree polynomial (when n=3). Example :- Monomial = x2 Binomial =3x2+2x Trinomial =5x4+3x2+8 Zero polynomial = all the coefficient of polynomial is zero called as zero polynomial We can do the following operations in internet solving polynomials Addition of polynomials Subtraction of polynomials Multiplication of polynomials Types of Polynomials Linear polynomials Quadratic polynomials Cubic polynomials Bi-quadratic polynomials Internet solving polynomials: Read More About Degree of Polynomial
The following sums are the example for internet solving polynomial Polynomial Examples Below are some examples on polynomials Example 1 :- Add the following two polynomials 5x3+3x2+2x+1 and 6x2+3x+2 Solution :- Given: 5x3+3x2+2x+1 and 6x2+3x+2 Addition of two polynomials = (5x3+3x2+2x+1) + (6x2+3x+2) = 5x3+3x2+2x+1 6x2+3x+2 (+) ---------------------------5x3+9x2+5x+3 ---------------------------Add the equal exponential variables = 5x3+9x2+5x+3
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