A.6.9.3 What is the Standard Form? What is the Factored Form?

Author:
Katie Akesson

The quadratic expression x2 + 4x + 3is written in standard form. Here are some other quadratic expressions. The expressions on the left are written in standard form and the expressions on the right are not. Written in standard form:      Not written in standard form: What are some characteristics of expressions in standard form?

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(x + 1)(x - 1) and (2x +3)x in the right column are quadratic expressions written in factored form. Why do you think that form is called factored form?

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A quadratic expression in standard form is defined as ax2 + bx + c. We refer to a as the coefficient of the squared term x2, b as the coefficient of the linear term x, and c as the constant term. A quadratic expression in factored form is a product of two factors that are each a linear expression. For example, (x + 1)(x - 1), (2x + 3)x, and x(4x) all have two linear expressions for their factors. An expression with two factors that are linear expressions and a third factor that is a constant, for example: 2(x + 2)(x - 1), is also in factored form.

How would you write (2x+ 3)x in standard form?

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The expression 2x2 + 3x only has two terms. Is it still in standard form?

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How would you write -4(x2 + 1/4x) + 7 in standard form?

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What are the values of the coefficients a and b for -4x2 - x + 7?

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What does it mean to expand a factored expression?

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How would you explain to a friend who is absent today how to write an equivalent expression for (x - 10)(x - 5)? What strategy (or strategies) would you suggest?

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