Factor Trinomials Factor Trinomials In this article, we study about factoring trinomials. Trinomials are defined in Mathematics an expression containing 3 unlike terms. For example, xz+y-2 is a trinomial, whereas x2-3X-X is not a trinomial as this can be simplified in to a binomial. So for an expression to be a trinomial, we have 3 terms which cannot be further simplified. The degree of the trinomial is the highest degree in the expression. If the highest degree of all variables put together is 2 then it is called quadratic and if it is 3, then it is cubic function. Factoring trinomials is complicated than factoring numbers because numbers are all like terms, which we can add , subtract, etc. Also numbers we are familiar with tables and know the divisibility rules for 2, 3, 9, etc. But for expressions also we can become well-versed by continuous practice and doing exercises. Understanding the concept of factoring trinomials whenever it is of a square form, or whether +ve sign is there, or -ve sign is there, if we understand then factorization will be one step further. The advantage of trinomial is that its degree normally does not exceed 2. Hence quadratic formula we can apply if we cannot find exact splitting up of the x term.
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Eg: x2-2x-1 is of degree 2 whereas x4-x2-1 is a trinomial of degree 4. Factoring trinomials can be done in any of the following ways. We already know these identities as (a+b)2 = a2+2ab+b2 (a-b)2 = a2-2ab+b2 (x+a)(x+b) = x2+x(a+b)+ab These can be applied in reverse to factoring trinomials of this form. Example: Factorize x2-6x+9 This is of the form x2-2(x)(3)+32 . So factors are (x+3)2 Next is factorise 25x2-50x+1 = (5x)2-2(5x)(1)+1 = (5x-1)2 Thus these type of terms can be easily factored. Hence given a polynomial we check whether it is a quadratic with on variable, if it is so, check whether first term and last term is a square. If it is satisfied then check for middle term whether it is of the form 2ab. Thus this identity in reverse is used in factoring trinomials, For expressions of the form say x2-6x+5 , we have 5=5*1, and 6 =5+1, thus the third identity can be applied here to factorize. So the expression = (x-5)(x-1). Thus these three identities are helpful in Factoring trinomials.
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Simplify Algebraic Expressions Simplify Algebraic Expressions The algebraic expressions have the variables and the constants. The algebraic expressions are the finite combination of the symbols that are formed according to the rules of the context. The algebra is an expression which is used to designate the value for the given values in the expression. The expression might be depending on the values assigned to the values assigned in the expression. The expression is the syntactic concept in the algebra. The online provides the connectivity between the tutors and the students. This article has the information about learn online algebraic expressions. In mathematics, an algebraic expression is an expression that contains variables and a finite number of algebraic operations (addition, subtraction, multiplication, division and exponentiation to a rational exponent). A rational algebraic expression (or rational expression) is an algebraic expression that can be written as a quotient of polynomials, such as . An irrational algebraic expression is one that is not rational, such as
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Some but not all polynomial equations with rational coefficients have a solution that is an algebraic expression with a finite number of operations involving just those coefficients (that is, can be solved algebraically). This can be done for all such equations of degree one, two, three, or four; but for given n≼5 it can be done for some equations but not for others. Example 2 Compute the factors for the expression x2+ 76x+ 1440. Solution : The given expression is x2+ 76x+ 1440. Step 1: x2+ 76x+ 1440 = x2+36x+ 40x+ (36x 40) Step 2: x2+ 76x+ 1440 = x(x+36) + 40(x +36) Step 3: x2+ 76x+ 1440 = (x+36) (x+40) Step 4: x+36 and x+40 The factors for the given expression x2+ 76x+ 1440 are (x +36) and (x +40). Example 3 Simplify the expression 24xy + 10 x2y + 14 x y + 16 x2y + 10 x y. Solution : The given expression is 24xy + 10 x2y + 14 x y + 16 x2y + 10 x y. Step 1: 24xy + 10 x2y + 14 x y + 16 x2y + 10 x y = x y (24 +14 +10) + x2y (10+ 16) Step 2: 24xy + 10 x2y + 14 x y + 16 x2y + 10 x y = 48 x y + x2y (10+ 16) Step 3: 24xy + 10 x2y + 14 x y + 16 x2y + 10 x y = 48 x y + 26 x2y The value for the given expression 12xy + 13 x2y + 16 x y + 20 x2y is 48 x y + 26 x2y.
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