How do you factor #x^2 - 45x + 450#?

1 Answer
George C.
Sep 26, 2016

#x^2-45x+450 = (x-30)(x-15)#

Explanation:

Note that #45=30+15# and #450 = 30*15#

Hence:

#x^2-45x+450 = (x-30)(x-15)#

Alternatively, you could find it by completing the square:

#4(x^2-45x+450) = 4x^2-180x+1800#

#color(white)(4(x^2-45x+450)) = (2x-45)^2-45^2+1800#

#color(white)(4(x^2-45x+450)) = (2x-45)^2-2025+1800#

#color(white)(4(x^2-45x+450)) = (2x-45)^2-225#

#color(white)(4(x^2-45x+450)) = (2x-45)^2-15^2#

#color(white)(4(x^2-45x+450)) = ((2x-45)-15)((2x-45)+15)#

#color(white)(4(x^2-45x+450)) = (2x-60)(2x-30)#

#color(white)(4(x^2-45x+450)) = 4(x-30)(x-15)#

So dividing both ends by #4# we find:

#x^2-45x+450 = (x-30)(x-15)#

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