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> Polynomials : Recognizing trinomial squares Quiz
Polynomials : Recognizing trinomial squares Quiz
Quiz
*Theme/Title:
Recognizing trinomial squares
* Description/Instructions
This quiz focuses on recognizing trinomial squares. A trinomial that is the square of a binomial is called a trinomial square, or a perfect-square trinomial. There are two types of expressions that can be written as trinomial squares:
A^2 + 2AB + B^2 = (A + B)^2
A^2 - 2AB + B^2 = (A - B)^2
To recognize whether or not an expression is a trinomial square, the first step is to examine the two expressions A^2 and B^2. These two expressions must be squares, for example, 9, y^2, 25x^4, 49t^2. (When the coefficient is a perfect square and the power of the variable is even, then the expression is a perfect square.) The next step is to make sure there is no minus sign before A^2 or B^2. The final step is to multiply A and B and double the result. If this gives the remaining term or its opposite, then this is a trinomial square.
Example:
x^2 + 8x + 16
We know that x^2 and 16 are squares.
There is no minus sign before x^2 or 16
If we multiply the square roots, x and 4, and double the product, we get the remaining term: 2*x*4 = 8x.
Therefore, x^2 + 8x + 16 = (x + 4)^2 is a trinomial square.
Group:
Algebra
Algebra Quizzes
Topic:
Polynomials
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