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 squaretrinomials.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...)
(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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