Question

1. (45x^{8}+30x^{6}) (15x^{6}(3x^{2} + 2)) 2. (-15x^{9}+10x^{3}) 3. (-18x^{5}-24x^{4}) 4. (2x^{10}+18x^{2}) 5. (-12x^{8}+54x^{2}) 6. (12x^{10}+24x^{4}) 7. (-8x^{7}+24x^{5}) 8. (-6x^{9}+18x^{8})

Explanation:

Step1: Find GCF for coefficients and variables

For each polynomial, find the greatest - common factor (GCF) of the coefficients and the lowest - power of the variable.

Step2: Factor out the GCF

Factor out the GCF from each term of the polynomial.

1. For \(-15x^{9}+10x^{3}\), the GCF of 15 and 10 is 5, and the GCF of \(x^{9}\) and \(x^{3}\) is \(x^{3}\). So, \(-15x^{9}+10x^{3}= - 5x^{3}(3x^{6}-2)\)
2. For \(-18x^{5}-24x^{4}\), the GCF of 18 and 24 is 6, and the GCF of \(x^{5}\) and \(x^{4}\) is \(x^{4}\). So, \(-18x^{5}-24x^{4}=-6x^{4}(3x + 4)\)
3. For \(2x^{10}+18x^{2}\), the GCF of 2 and 18 is 2, and the GCF of \(x^{10}\) and \(x^{2}\) is \(x^{2}\). So, \(2x^{10}+18x^{2}=2x^{2}(x^{8}+9)\)
4. For \(-12x^{8}+54x^{2}\), the GCF of 12 and 54 is 6, and the GCF of \(x^{8}\) and \(x^{2}\) is \(x^{2}\). So, \(-12x^{8}+54x^{2}=-6x^{2}(2x^{6}-9)\)
5. For \(12x^{10}+24x^{4}\), the GCF of 12 and 24 is 12, and the GCF of \(x^{10}\) and \(x^{4}\) is \(x^{4}\). So, \(12x^{10}+24x^{4}=12x^{4}(x^{6}+2)\)
6. For \(-8x^{7}+24x^{5}\), the GCF of 8 and 24 is 8, and the GCF of \(x^{7}\) and \(x^{5}\) is \(x^{5}\). So, \(-8x^{7}+24x^{5}=-8x^{5}(x^{2}-3)\)
7. For \(-6x^{9}+18x^{8}\), the GCF of 6 and 18 is 6, and the GCF of \(x^{9}\) and \(x^{8}\) is \(x^{8}\). So, \(-6x^{9}+18x^{8}=-6x^{8}(x - 3)\)

Answer:

1. \(-5x^{3}(3x^{6}-2)\)
2. \(-6x^{4}(3x + 4)\)
3. \(2x^{2}(x^{8}+9)\)
4. \(-6x^{2}(2x^{6}-9)\)
5. \(12x^{4}(x^{6}+2)\)
6. \(-8x^{5}(x^{2}-3)\)
7. \(-6x^{8}(x - 3)\)