| Background
What does "factor a quadratic expression" mean? It means to write
the quadratic expression
as the product of two linear expressions. In symbols, to factor
x2 + bx + c, means to find the numbers p and q such that p + q
= b
and pq = c.
x2 + bx + c = (x + p)(x + q)
Example:
x2 + 7x + 10 = (x + 5)(x + 2)
5 + 2 = 7 and (5)(2) = 10
If we have a quadratic expression whose leading coefficient is not 1,
like ax2 + bx + c where a ≠ 1, what we need to do in order to
factor it is find the
factors of a and and c and so that the
sum of the outer and inner products (mq and pn) is b.
In symbols,
ax2 + bx + c = (mx + p)(nx + q) |
Warm-Up 5x2 - 18x - 8 matches
(5x + 2)(x - 4).
“Because the last term in the quadratic expression
is negative, the signs of the constant factors will be
different. The factor pair for 5 is 5 and 1. The factor
pairs for 8 are 8 and 1, and 4 and 2. Because 5 times
4 is 20, 2 times 1 is 2, and -20 plus 2 is -18, the
factored expression is (5x + 2)(x - 4).â€
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