Question
Factories:
$x^2- 11x - 42$
$x^2- 11x - 42$
✓
Answer
To factories $x^2- 11x - 42,$ we will find two number $p$ and $q$ such that $p + q = -11$ and $pq = -42$
Now,
$3 + (-14) = -22$ And $3 x (-14) = 42$
Splittiong the middle term -11x in the given quadratic as $-14x + 3x$, we get:
$ x^2-11 x-42=x^2-14 x+3 x-42 $
$ =\left(x^2-14\right)+(3 x-42) $
$ =x(x-14)+3(x-14) $
$ =(x-14)(x+3) $
Now,
$3 + (-14) = -22$ And $3 x (-14) = 42$
Splittiong the middle term -11x in the given quadratic as $-14x + 3x$, we get:
$ x^2-11 x-42=x^2-14 x+3 x-42 $
$ =\left(x^2-14\right)+(3 x-42) $
$ =x(x-14)+3(x-14) $
$ =(x-14)(x+3) $
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