Factor the Polynomial Factoring Polynomial refers to factoring a polynomial into irreducible polynomials over a given field. It gives out the factors that together form a polynomial function. A polynomial function is of the form xn + xn -1 + xn - 2 + . . . . + k = 0, where k is a constant and n is a power. Polynomials are expressions that are formed by adding or subtracting several variables called monomials. Monomials are variables that are formed with a constant and a variable of some degree. Examples of monomials are 5x3, 6a2. Monomials having different exponents such as 5x3 and 3x4 cannot be added or subtracted but can be multiplied or divided by them. Any polynomial of the form F(a) can also be written as F(a) = Q(a) x D (a) + R (a) using Dividend = Quotient x Divisor + Remainder. Know More About Finding Roots of Polynomials
If the polynomial F(a) is divisible by Q(a), then the remainder is zero. Thus, F(a) = Q(a) x D(a). That is, the polynomial F(a) is a product of two other polynomials Q(a) and D(a). For example, 2t + 6t2 = 2t x (1 + 3t). Variables, Exponents, Parenthesis and Operations (+, -, x, /) play an important role in factoring a polynomial. Factorization by dividing the expression by the GCD of the terms of the given expression: GCD of a polynomial is the largest monomial, which is a factor of each term of the polynomial. It involves finding the Greatest Common Divisor (GCD) or Highest Common Factor (HCF) of the terms of the expression and then dividing each term by its GCD. Therefore the factors of the given expression are the GCD and the quotient thus obtained. Example 1: Factorize : 2x3 – 6x2 + 4x. Solution: Factors of 2x3 are 1, 2, x, x2, x3,2x, 2x2, 2x3 Learn More About what is a trinomial
Factors of 6x2 are 1, 2,3, 6, x, x2, 2x, 2x2 ,3x, 3x2 ,6x, 6x2 Factors of 4x are 1,2,4,x,2x,4x. Thus the GCD of the above terms is 2x. Dividing 2x3 , -6x2 and 4x by 2x, we get x2 - 3x + 2 Then the GCD becomes one factor and the quotient is the other factor. 2x3 – 6x2 + 4x = 2x .(x2 - 3x + 2) Therefore the factors of 2x3 – 6x2 + 4x are 2x and (x2 - 3x + 2) Thus, 2x3 – 6x2 + 4x = 2x .(x2 - 3x + 2) Factorization by grouping the terms of the expression:
Simplify Polynomials Simplify Polynomials 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: 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 Read More About Solve Absolute Value Equations
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 (+)
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