Is it possible to factor $y= x^2 + 4x -21$ ? If so, what are the factors?

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Answer 1 · 2018-06-18T09:39:37

$(x+7)(x-3)$

$"the factors of - 21 which sum to + 4 are + 7 and - 3"$

$x^2+4x-21=(x+7)(x-3)$

Answer 2 · 2018-06-18T09:55:05

Yes: $(x+7)(x-3)$

You can do it solving: $x^2+4x-21=0$

$x^2+4x-21=0$

$a=1, b=4, c=-21$

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{-(4)\pm \sqrt{(4)^2-4(1)(-21)}}{2(1)}$

$x=\frac{-4\pm \sqrt{16+84}}{2(1)}$

$x=\frac{-4\pm \sqrt{100}}{2}$

$x=\frac{-4\pm 10}{2}$
then
$x_1=\frac{-4+10}{2}=\frac{6}{2}=3$
$x_2=\frac{-4-10}{2}=\frac{-14}{2}=-7$
And

$x^2+bx+c=(x-x_1)(x-x_2)$
Or
$x^2+4x-21=(x-3)(x-(-7))$

$x^2+4x-21=(x-3)(x+7)$
Q.E.D.

Is it possible to factor y= x^2 + 4x -21 y= x^2 + 4x -21 ? If so, what are the factors?