QQuestionMathematics
QuestionMathematics
Explain why 3x^2 can be said to be in both standard form and factored form.
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Answer
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Step 1:: Identify the standard form and factored form of the expression
The expression given is 3x^2. In elementary algebra, the standard form of a quadratic function is f(2$) = ax^2 + bx + c, where a, b, and c are constants. So, 3x^2 can be considered in standard form with a = 3, b = 0, and c = 0.
Step 2:: Understand factored form for quadratic expressions
A quadratic expression in factored form is typically written as a product of linear factors, such as (px + q)(rx + s). However, the expression 3x^2 does not have any linear factors since it is a perfect square.
Step 3:: Recognize special cases of factored form
In some contexts, expressions that are perfect squares, like 3x^2, can be considered as "factored" because they can be written as a square of a binomial. That is, 3x^2 = (√3x)^2. Here, (√3x) is a binomial, and its square results in 3x^2.
Final Answer
The expression 3x^2 can be considered in both standard form and factored form because it can be written in the standard form of a quadratic function (ax^2 + bx + c), and it can also be represented as a square of a binomial (√3x)^2, which is a special case of factored form for quadratic expressions.
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