Remove the largest possible common factor. Check your answer by multiplication.
15x^5-9x^4-12x
Factor out the greatest common factor.
3x(5x^4-3x^3-4x)
Check your answer by multiplication.
3x(5x^4-3x^3-4x) = 15x^5-9x^4-12x
To factor out the greatest common factor, we need to find the largest possible factor that can be divided evenly into each term of the expression.
The expression given is 15x^5 - 9x^4 - 12x.
Let's list the factors of the coefficients (15, 9, 12) and find the factors of x to determine the greatest common factor.
Factors of 15: 1, 3, 5, 15
Factors of 9: 1, 3, 9
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of x: x
From the factors listed above, the largest factor that can be divided evenly into each term is 3.
So, we can factor out 3 from each term:
3(5x^5 - 3x^4 - 4x)
To check our answer, we can multiply the factored expression by the greatest common factor and see if we get the original expression:
3 * (5x^5 - 3x^4 - 4x) = 15x^5 - 9x^4 - 12x,
which is the original expression. Therefore, our factored form is correct.