Is it possible to factor y= x^2 + 4x -21 y=x2+4x−21? If so, what are the factors?

2 Answers
Jim G.
Jun 18, 2018

(x+7)(x-3)(x+7)(x−3)

Explanation:

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

x^2+4x-21=(x+7)(x-3)x2+4x−21=(x+7)(x−3)

Arnoldo B.
Jun 18, 2018

Yes: (x+7)(x-3)(x+7)(x−3)

Explanation:

You can do it solving: x^2+4x-21=0x2+4x−21=0

x^2+4x-21=0x2+4x−21=0

a=1, b=4, c=-21a=1,b=4,c=−21

x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}x=−b±√b2−4ac2a

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

x=\frac{-4\pm \sqrt{16+84}}{2(1)}x=−4±√16+842(1)

x=\frac{-4\pm \sqrt{100}}{2}x=−4±√1002

x=\frac{-4\pm 10}{2}x=−4±102
then
x_1=\frac{-4+10}{2}=\frac{6}{2}=3x1=−4+102=62=3
x_2=\frac{-4-10}{2}=\frac{-14}{2}=-7x2=−4−102=−142=−7
And

x^2+bx+c=(x-x_1)(x-x_2)x2+bx+c=(x−x1)(x−x2)
Or
x^2+4x-21=(x-3)(x-(-7))x2+4x−21=(x−3)(x−(−7))

x^2+4x-21=(x-3)(x+7)x2+4x−21=(x−3)(x+7)
Q.E.D.

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