How do you factor #y= x^2-x-20# ?

2 Answers
Nghi N.
Mar 14, 2016

y = (x + 4)( x- 5)

Explanation:

Find 2 numbers knowing sum (-1) and product (-20). It is the factor pairs (4, - 5). The 2 numbers are 4 and -5
y = (x + 4)(x - 5)

Costas C.
Mar 14, 2016

Find its solutions and write it as:

#ax^2+bx+c=a(x-x_1)(x-x_2)#

Answer is:

#x^2-x-20=(x-5)(x+4)#

Explanation:

If you find all it's solutions #(x_1,x_2,x_3...)# you can write it as a product of its solutions. If the polynomial has two solutions #(x_1,x_2)# you can solve it like this:

#ax^2+bx+c=a(x-x_1)(x-x_2)#

For #y=x^2-x-20# the two solutions:

#y=0#

#x^2-x-20=0#

#a=1#
#b=-1#
#c=-20#

#Δ=(-1)^2-4*1*(-20)=81#

#x_(1,2)=(-b+-sqrt(Δ))/(2a)=(-(-1)+-sqrt(81))/(2*1)=(1+-9)/2#

#x_1=5#

#x_2=-4#

Therefore the equation can be written:

#x^2-x-20=a(x-x_1)(x-x_2)=(x-5)(x+4)#

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