Algebra I: Factoring a quadratic into binomials
This is a free lesson from our course in Algebra I
This lesson shows you how to factor a quadratic into binomials. As is the case in Algebra many times, the overview provided here in text might seem a little complicated, but don't worry -- it will be easy to follow once you hear the instructor explain it in the video provided above. Some quadratics can be factored into two identical binomials. Such quadratics are called perfect square trinomials.As quadratic expression is the product of two binomials, factoring a quadratic means breaking the quadratic back into its binomial parts. Here factoring is done using the rule of LIOF (FOIL in reverse). (More text below video...)
<h2> Factoring a quadratic into binomials - Watch video (Algebra I)</h2> <p> factoring, quadratic, video, rule, FOIL, binomial, identical, square, quadratic equation, factor, product, perfect square trinomials, rule, factoring trinomials, difference of squares, online algebra, practice questions, quizzes</p> <p> The factoring of x<SUP>2</SUP> + (a + b)x + ab will result into (x + a) (x + b), the difference of two squares: (x<SUP>2</SUP> - c<SUP>2</SUP>) = (x + c) (x - c).</p>
Other useful lessons:
Factoring an expression of exponents with the same base
Factoring a quadratic using the perfect square method
Factoring a 3rd degree polynomial
(Continued from above) A couple of general rules to keep in mind:
• the factoring of x2 + (a + b)x + ab will result into (x + a)(x + b). For example, the two factors of x2 + 5x + 6 are (x + 2)(x + 3)
• another common type of algebraic factoring is called the difference of two squares: (x2 - c2) = (x + c)(x - c). For example: factors of   x2 - 4 are (x + 2)(x - 2)
The Procedure:
Given a general quadratic trinomial ax2 + bx + c
• find the product ac.
• find two numbers p and q such that pq = ac (p and q are factors of the product of the coefficient of x2 and the constant term) AND p +   q = b (p and q add to give the coefficient of x)
• rewrite the quadratic as ax2 + px + qx + c
• group the two pairs of terms that have common factors and simplify. (ax2 + px) + (qx + c) x(ax + p) + (qx + c) (note: because of the   way you choose p and q, you will be able to factor a constant out of the second parentheses, leaving you with two identical expressions   in parentheses).
• remember that this won’t work for all quadratic trinomials, because not all quadratic trinomials can be factored into products of   binomials with integer coefficients. If you have a non-factorable trinomial, you will not be able to do the second step above.
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