![]() We can do the same to expand an expression with a sum and a difference, such as \((x+5)(x-2)\), or to expand an expression with two differences, for example, \((x-4)(x-1)\). Cant get enough of Sal factoring simple quadratics Heres a handful of examples just for you Created by Sal Khan and CK-12 Foundation. Unit 8 Absolute value equations, functions, & inequalities. The values, a, r, and s, are values that also determine the shape and position of the parabola. Unit 2 Solving basic equations & inequalities (one variable, linear) Unit 3 Linear equations, functions, & graphs. In a previous lesson we saw how to use a diagram and to apply the distributive property to multiply two linear expressions, such as \((x+3)(x+2)\). Factoring quadratics is a method of expressing the quadratic equation ax 2 + bx + c 0 as a product of its linear factors as (x - k) (x - h), where h, k are the roots of the quadratic equation ax 2 + bx + c 0. The factored form of the equation for a quadratic relation is y a(x - r)(x - s), a product of three factors. When the quadratic expression is a product of two factors where each one is a linear expression, this is called the factored form.Īn expression in factored form can be rewritten in standard form by expanding it, which means multiplying out the factors. The function \(f\) can also be defined by the equivalent expression \((x+2)(x+1)\). We refer to \(a\) as the coefficient of the squared term \(x^2\), \(b\) as the coefficient of the linear term \(x\), and \(c\) as the constant term. In general, standard form is \(\displaystyle ax^2 + bx + c\) Factoring Using the Middle Term This method is similar to the grouping method applied to simpler forms of a quadratic expression. The quadratic expression \(x^2 + 3x + 2\) is called the standard form, the sum of a multiple of \(x^2\) and a linear expression ( \(3x+2\) in this case). If a quadratic equation can be factored, it is written as a product of linear terms. Therefore, we have factored the quadratic equation completely. For example, a quadratic function \(f\) might be defined by \(f(x) = x^2 + 3x + 2\). ![]() A quadratic function can often be represented by many equivalent expressions.
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