How do you factor the expression x2+17x+52?

1 Answer
George C.
Apr 2, 2016

x2+17x+52=(x+13)(x+4)

Explanation:

Note that 52=13×4 and 17=13+4

So: x2+17x+52=(x+13)(x+4)

In general we find (x+a)(x+b)=x2+(a+b)x+ab

So if we can find a pair of numbers a,b whose product is the constant term and whose sum is the coefficient of the middle term, then we can factorise the quadratic as (x+a)(x+b)


Alternative method

x2+17x+52 is in the form ax2+bx+c with a=1, b=17 and c=52.

This quadratic has zeros given by the quadratic formula:

x=−b±√b2−4ac2a

=−17±√172−(4⋅1⋅52)2⋅1

=−17±√289−2082

=−17±√812

=−17±92

That is: x=−13 or x=−4

Hence the quadratic has corresponding factors (x+13) and (x+4)

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