# How do you determine the binomial factors of #x^3-x^2-49x+49#?

##### 1 Answer

The binomial factors of

#(x^2-49)# ,#(x-1)# ,#(x-7)# ,#(x+7)#

#### Explanation:

The given cubic factors by grouping:

#x^3-x^2-49x+49 = (x^3-x^2)-(49x-49)#

#color(white)(x^3-x^2-49x+49) = x^2(x-1)-49(x-1)#

#color(white)(x^3-x^2-49x+49) = (x^2-49)(x-1)#

Note that both

The difference of squares identity can be written:

#a^2-b^2 = (a-b)(a+b)#

Hence we find:

#x^2-49 = x^2-7^2 = (x-7)(x+7)#

So

Multiplying either of these by

#(x-7)(x-1) = x^2-8x+7#

#(x+7)(x-1) = x^2+6x-7#

The complete list of polynomial factors of

#x^3-x^2-49x+49#

#x^2-49#

#x^2-8x+7#

#x^2+6-7#

#x-7#

#x+7#

#x-1#

#1#