what are the factors of an algebraic expression?
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Factor: Something which is multiplied by something else. A factor can be a number, variable, term, or a longer expression. For example, the expression 7x(y+3) has three factors: 7 , x , and (y+3) .
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In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value. The most basic and common algebraic equations in math consist of one or more variables.
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Algebraic expressions are combinations of variables , numbers, and at least one arithmetic operation. For example, 2x+4y−9 is an algebraic expression. Term: Each expression is made up of terms. A term can be a signed number, a variable, or a constant multiplied by a variable or variables.
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If you can find its roots, you can find its factors. In symbols, the factor theorem states that if x – c is a factor of the polynomial f(x), then f(c) = 0. The variable c is a zero or a root or a solution — whatever you want to call it (the terms all mean the same thing).
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Factoring Quadratic Equations - Common Factors. ... In this algebra lesson, we will discuss how factoring can be used to solve Quadratic Equations, which are equations of the form: ax2 + bx + c = 0 where a, b and c are numbers and a ≠ 0. The simplest way to factoring quadratic equations would be to find common factors.
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All polynomials are algebraic expressions, but all algebraic expressions are not polynomials. For an algebraic expression to be a polynomial, It must not have a variable inside the radical symbol. It must have no negative exponents.
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Another useful way of thinking about polynomial and rational expressions is that polynomial expressions are those algebraic expressions that can be evaluated using a finite number of additions and multiplications (and subtractions), whereas rational expressions may also require division for their evaluation.
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To factorize the quadratic expression x2−9x+20 , one must find the two numbers that add together to give 9, and multiply together to give 20. Those two numbers are 4 and 5, which factor into the expression (x−4)(x−5) .
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The expressions in which the numbers, or variables, or both, are connected by operational signs (+, - etc.) are called algebraic expressions. For example 5, 4x, a+b, x−y etc.
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For example, 2(3 + 8) is a numeric expression. Algebraic expressions include at least one variable and at least one operation (addition, subtraction, multiplication, division). For example, 2(x + 8y) is an algebraic expression.
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The number of times a given factor appears in the factored form of the equation of a polynomial is called the multiplicity. The zero associated with this factor, x=2 , has multiplicity 2 because the factor (x−2) occurs twice. The x-intercept x=−1 is the repeated solution of factor (x+1)3=0 ( x + 1 ) 3 = 0 .
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Therefore, when solving quadratic equations by factoring, we must always have the equation in the form "(quadratic expression) equals (zero)" before we make any attempt to solve the quadratic equation by factoring. Note that "x = 3, 4" means the same thing as "x = 3 or x = 4"; the only difference is the formatting.
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An algebraic expression is a mathematical expression that consists of variables, numbers and operations. The value of this expression can change.
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['Factors of 8: 1, 2, 4, 8.', 'Factors of 12: 1, 2, 3, 4, 6, 12.', 'Common factors of 8 and 12: 1, 2, 4.', 'Greatest common factor of 8 and 12: 4.']
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An expression is in factored form only if the entire expression is an indicated product. Factoring is a process that changes a sum or difference of terms to a product of factors. ... The greatest common factor is the greatest factor common to all terms.
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An expression containing variables, numbers, and operation symbols is called an algebraic expression. is an example of an algebraic expression. Each expression is made up of terms. A term can be a signed number, a variable, or a constant multiplied by a variable or variables. ... In the term 5x, the coefficient is 5.
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Binomial factors are polynomial factors that have exactly two terms. Binomial factors are interesting because binomials are easy to solve, and the roots of the binomial factors are the same as the roots of the polynomial. Factoring a polynomial is the first step to finding its roots.