Find the greatest common factor (GCF/HCF) of the polynomials $15a^3, -45a^2$ and $-150a$.

Given:

Given polynomials are $15a^3, -45a^2$ and $-150a$.

To do:

We have to find the greatest common factor of the given polynomials.

Solution:

GCF/HCF:

A common factor of two or more numbers is a factor that is shared by the numbers. The greatest/highest common factor (GCF/HCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.

The numerical coefficient of $15a^3$ is $15$

The numerical coefficient of $-45a^2$ is $45$

The numerical coefficient of $-150a$ is $150$

This implies,

$15=3\times5$

$45=3\times3\times5$

$150=2\times3\times5\times5$

HCF of $15, 45$ and $150$ is $3\times5=15$

The common variable in the given polynomials is $a$.

The power of $a$ in $15a^3$ is $3$

The power of $a$ in $-45a^2$ is $2$

The power of $a$ in $-150a$ is $1$

The monomial of common literals with the smallest power is $a$.

Therefore,

The greatest common factor of the given polynomials is $15a$.