# Can #y= x^2+7x-30 # be factored? If so what are the factors ?

##### 1 Answer

Jan 4, 2016

#x^2+7x-30 = (x+10)(x-3)#

#### Explanation:

Find a pair of factors of

#x^2+7x-30 = (x+10)(x-3)#

This has discriminant

#Delta = b^2-4ac = 7^2-(4xx1xx-30) = 49+120 = 169 = 13^2#

Since this is a perfect square, the quadratic has two linear factors with rational coefficients.

Rather than search for a suitable pair of factors of

#x = (-b+-sqrt(b^2-4ac))/(2a) = (-b+-sqrt(Delta))/(2a)#

#=(-7+-13)/2#

That is

Hence factors