This shortcut can help you identify quadratic polynomials that do not factor ‘‘nicely’’ without spending too much time on them. The next three examples are quadratic polynomials that do not factor ‘‘nicely.
Quadratic polynomials of the form x2 – c2 are
called the difference of two squares. We can use the shortcut on x2 –
c2 = x2 + 0x – c2. The factors of c2
must have a difference of 0. This can only happen if they are the same, so the
factors of c2 we want are c and c.
Examples
When the sign
between x2 and c2 is plus, the quadratic cannot be
factored using real numbers.
Practice
Solutions
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Mathematician
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