Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor the polynomial by its greatest common monomial factor.

12k^(3)-30k^(4)=

Factor the polynomial by its greatest common monomial factor. $\newline$ $12 k^{3}-30 k^{4}=$

View step-by-step help

View step-by-step help

Factor out a monomial

Full solution

Q. Factor the polynomial by its greatest common monomial factor.

\newline

12 k^{3}-30 k^{4}=

Identify GCF: Identify the greatest common factor (GCF) of the terms $12k^3$ and $30k^4$ . The factors of $12$ are $1, 2, 3, 4, 6,$ and $12$ . The factors of $30$ are $1, 2, 3, 5, 6, 10, 15,$ and $30$ . The common factors of $12$ and $30$ are $30k^4$ $0$ and $30k^4$ $1$ . The highest of these is $30k^4$ $1$ . Both terms also have the variable $30k^4$ $3$ raised to a power. The lowest power of $30k^4$ $3$ that appears in both terms is $30k^4$ $5$ . Therefore, the GCF of $12k^3$ and $30k^4$ is $30k^4$ $8$ .
Find Factors: Divide each term by the GCF to find the remaining factors. $\newline$ For the first term, $12k^3$ divided by $6k^3$ is $2$ . $\newline$ For the second term, $30k^4$ divided by $6k^3$ is $5k$ .
Write Factored Form: Write the original polynomial as the product of the GCF and the remaining factors. $\newline$ The factored form of the polynomial is $6k^3(2 - 5k)$ .

More problems from Factor out a monomial

Question

Find the greatest common factor.

\newline

9v^3, 6v^3

\newline

\newline

Write your answer as a constant times a product of single variables raised to exponents.

\newline

\underline{\hspace{1cm}}

Posted 5 months ago

Question

Factor out the greatest common factor. If the greatest common factor is

1

, just retype the polynomial.

\newline

6x^3 + 9x^2

\newline

Posted 5 months ago

Question

\newline

k^2 + 9k + 18

\newline

Posted 5 months ago

Question

\newline

9j^2 - 16

\newline

Posted 5 months ago

Question

\newline

j^3 + 2j^2 + 5j + 10

Posted 5 months ago

Question

x^4 + 6x^2 + 9

\newline

All factors in your answer should have integer coefficients.

\newline

Posted 9 months ago

Question

\newline

z^2 + 13z + 22

\newline

Posted 8 months ago

Question

Simplify the expression:

\newline

5x + 9x - 4x - 2x

\newline

Posted 10 months ago

Question

3 - 3^2

Posted 10 months ago

Question

5 - 5^2

Posted 7 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant