What is the complete factorization of the polynomial below x^3+5x^2-x-5

Accepted Solution

Answer:(x+5)(x-1)(x+1)Step-by-step explanation:Let's attempt factoring by grouping:So what this means we first want to group the first two terms together and second two terms together, like so:(x^3+5x^2)+(-x-5)Now we factor what we can from each pair:x^2(x+5)+1(-x-5)Notice x+5 doesn't appear to be the same as -x-5 so we should factor out -1 instead of 1 in the second pair of terms:x^2(x+5)-1(x+5)You have two terms: x^2(x+5) and -1(x+5); they have a common factor of (x+5) so we can factor it out:(x+5)(x^2-1)You can actually factor this more because x^2-1 is a difference of squares.The formula for factoring a difference of squares is u^2-v^2=(u-v)(u+v).So the factored form of x^2-1 is (x-1)(x+1).So the complete factored form of our expression we had initially is (x+5)(x-1)(x+1).