Question

K(x) = (x + 1)2 – 25
What would this be rewritten in factored form?

Answer 1

`k(x)=(x-4)(x+6)`

Explanation:

`k(x)=(x+1)^2-25\\\\`

to factorize it you have to remember the difference of squares that says

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

so we have

`(x+1)^2\\\\(x+1)^2=a^2\\\\25\longrightarrow 5^2\\\\5^2=b^2\\\\`

and we apply the formula

`(x+1)^2-25=[(x+1)-5][(x+1)+5]\\\\=(x+1-5)(x+1+5)\\\\=(x-4)(x+6)`

so there you have it

`k(x)=(x-4)(x+6)`