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An expression obtained from the square of a binomial equation is a perfect square trinomial. An expression is said to a perfect square trinomial if it takes the form ax² + bx + c and satisfies the condition b² = 4ac.

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When an expression can be viewed as the difference of two perfect squares, i.e. a²-b², then we can factor it as (a+b)(a-b). For example, x²-25 can be factored as (x+5)(x-5). This method is based on the pattern (a+b)(a-b)=a²-b², which can be verified by expanding the parentheses in (a+b)(a-b).

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Factoring Quadratics of the Form ax² + bx + c

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Factoring Quadratics of the Form ax² + bx + c

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This section explains how to factor expressions of the form ax² + bx + c, where a, b, and c are integers. First, factor out all constants which evenly divide all three terms. If a is negative, factor out -1. This will leave an expression of the form d (ax² + bx + c), where a, b, c, and d are integers, and a > 0.

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Factoring Quadratics of the Form x² + bx + c

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Factoring Quadratics of the Form x² + bx + c

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To factor polynomials of the form x ² + bx + c, begin with two pairs of parentheses with x at the left of each. Next, find two integers whose product is c and whose sum is b and place them at the right of the parentheses. Factor x ² + 8 x + 12. Factor x ² – 7 x – 18.

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A common factor is a whole number which is a factor of two or more numbers.

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1. Multiply the First terms.

2. Multiply the Outer terms.

3. Multiply the Inner terms.

4. Multiply the Last terms.

5. Combine like terms, when possible.