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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 $15a$.
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