Question

Factor the polynomial by removing the common monomial factor: (X⁵+x⁴+x).

a) (X(X⁴+x³+1))
b) (X²(X³+x²+1))
c) (X(X⁴+x³+1)(X+1))
d) (X²(X³+x²+1)(X+1))

Answer 1

To factor the polynomial (X⁵+x⁴+x), we factor out the greatest common factor, which is x, resulting in the answer x(X⁴+x³+1).

Step-by-step explanation:

To factor this polynomial, we look for the greatest common factor (GCF) among all the terms. Since each term includes an x, we can factor out an x from each term. The polynomial can be rewritten as x times the quantity of (X⁴+x³+1). Therefore, the correct factored form is x(X⁴+x³+1), which matches option (a). This factoring is based on the distributive property, which tells us that a(b+c)=ab+ac. If we distribute the x back into the parentheses, we would get the original polynomial back.