Answer :
Final answer:
The greatest common factor (GCF) of the polynomial 15x^3 - 45x^2 - 150x is 15x. This means that the polynomial can also be expressed as 15x(x^2 - 3x - 10).
Explanation:
The question is asking you to find the greatest common factor (GCF) of the polynomial 15x^3 - 45x^2 - 150x. The GCF is the highest number or expression that divides exactly into two or more numbers or algebraic expressions.
You can approach this by first factoring out the common factors between the coefficients of the given terms. The numbers 15, 45, and 150 all have a common factor of 15. Each term also has 'x' as a common factor, and we always take the smallest power of 'x', which in this case is 1.
Hence, the GCF of 15x^3, -45x^2, and -150x is 15x. Therefore, when the polynomial is factored fully it can be expressed as 15x(x^2 - 3x - 10).
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