Question

When a monomial is completely factorized, what is the possible degree of each factor?

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

Answer: (A), (B)

$1$

$\underset{–}{\text{Complete Factor of a Monomial}:}$
To factor a monomial completely, we write the coefficient as a product of primes and expand the variable part.

For example, to completely factor $15x^3,$ we can write the prime factorization of $15$ as $3\cdot 5$ and write $x^3$ as $x\cdot x\cdot x$. Therefore, the complete factorization of $15x^3$:$15x^3=3\cdot 5\cdot x\cdot x\cdot x$

As in above example, complete factorization of $15x^3$ results in constant factors and variable factors with degree one.

Therefore, when a monomial is factorized, possible degree of each factor could $\underset{–}{0}$ and $\underset{–}{1}.$