what is factored form in algebra?
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A factored form is a parenthesized algebraic expression. In effect a factored form is a product of sums of products … or a sum of products of sums … Any logic function can be represented by a factored form, and any factored form is a representation of some logic function. 6. Factored Form Examples.
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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. Sometimes, the first step is to factor out the greatest common factor before applying other factoring techniques.
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Factoring the Polynomial Write the equation (x2-2) as the difference of two squares employing the terms' square roots. The expression (x2-2) becomes (x-√2) (x+√2).
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[' Find the product of 1st and last term( a x c). 6 x 10 = 60.', ' Find the factors of 60 in such way that. addition or subtraction of that factors is. ... ', ' Write the center term using the sum of the. ... ', ' Group the terms to form pairs - the first two. ... ', ' Factor out the shared (common) binomial parenthesis.']
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Quadratic functions can be written in three forms. The parameters and are the roots of the function (the x-intercepts of the graph ). Converting a quadratic function to factored form is called factoring. ... The parameter is the y-intercept, while the parameter is the slope of the tangent at 0.
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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 equation y = ax2 + bx + c is in factored form when it is written as. y = a(x - r. 1. )(x - r. 2.
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The factored form of the trinomial is (x + d )(x - e). Check: The binomials, when multiplied, should equal the original trinomial. If the middle term has the wrong sign, you most likely switched d and e. Switch the "+" and "-" sign in your binomials and check again.
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Difference of squares intro. When an expression can be viewed as the difference of two perfect squares, i.e. a²-b², then we can factor it as (a+b)(a-b). For example, x²-25 can be factored as (x+5)(x-5).
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To factorise a quadratic trinomial, find two numbers whose sum is equal to the coefficient of x, and whose product is equal to the independent term.
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Factoring is very helpful in simplifying expressions and solving equations involving polynomials. The greatest common factor (GCF) of two numbers is the largest number that divides evenly into both numbers. ... When factoring a polynomial expression, our first step should be to check for a GCF.
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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. Factor: Something which is multiplied by something else. A factor can be a number, variable, term, or a longer expression.
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Factoring is a step taken towards solving a quadratic equation. ... You cannot factor them, the only way to find the roots then, is by using the quadratic formula. Suppose you factor the quadratic polynomial as and . Then set them equal to zero and solve for , you will have and .
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An expression is in factored form only if the entire expression is an indicated product. ... The greatest common factor is the greatest factor common to all terms. An expression is completely factored when no further factoring is possible.
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['3 Sometimes, a quadratic equation cannot be factored Example: x 2 + 7x + 3 = 0 There is not a pair of numbers that multiply to give us 3, that will also add up to 7. ... ', '4 The Quadratic Formula can be used to solve for x on ANY quadratic equation ax 2 + bx + c = 0 X = -b ± b 2 – 4ac 2a.']
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The factored form of a polynomial means it is written as a product of its factors. The factors are also polynomials, usually of lower degree. Here is the same polynomial in factored form.
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If the quadratic looks particularly " ugly " use the quadratic formula. Quadratics with coefficients that involve roots would be one example of "ugly". After that (if the "ugly" rule doesn't apply): Factoring is usually faster and less prone to arithmetic mistakes (if you are working by hand).