Factoring Trinomials Special Cases

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What is a perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer. For example, x^2 and 16 are perfect squares.

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What is a perfect square trinomial?

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A perfect square trinomial is a polynomial that can be expressed in the form (a + b)^2 = a^2 + 2ab + b^2. For example, x^2 + 20x + 100 is a perfect square trinomial.

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How do you identify a perfect square trinomial?

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To identify a perfect square trinomial, check if it can be factored into the form (a + b)^2 or (a - b)^2, where a and b are terms derived from the original trinomial.

Front

What is the factored form of x^2 - 400?

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The factored form of x^2 - 400 is (x - 20)(x + 20), which is a difference of squares.

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What is the difference of squares?

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The difference of squares is a special case of factoring that applies to expressions of the form a^2 - b^2, which can be factored as (a - b)(a + b).

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How do you factor a trinomial of the form ax^2 + bx + c?

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To factor a trinomial of the form ax^2 + bx + c, look for two numbers that multiply to ac and add to b, then rewrite the middle term and factor by grouping.

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What is the factored form of 2n^2 + 13n + 15?

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The factored form of 2n^2 + 13n + 15 is (2n + 3)(n + 5).

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What is the significance of the coefficients in a trinomial?

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The coefficients in a trinomial (a, b, c) determine the shape and position of the parabola represented by the quadratic equation y = ax^2 + bx + c.

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What is the first step in factoring a perfect square trinomial?

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The first step in factoring a perfect square trinomial is to identify the square root of the first and last terms.

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What is the formula for factoring a perfect square trinomial?

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The formula for factoring a perfect square trinomial is (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2.