Question

1. $25z^{4}y^{6} + 45zx^{2} - 20z$
2. $56h^{4}j^{4}k - 48h^{3}j^{4} + 8h^{2}j^{3}k$
3. $28xy^{5}z^{8} + 7x^{6}y^{3}z^{2} + 56x^{3}y^{3}z^{3}$
4. $35x^{4} - 35x^{3} - 7yz$

Explanation:

Let's solve problem 11: \(25z^4y^6 + 45zx^2 - 20z\)

Step1: Identify the GCF

Find the greatest common factor (GCF) of the terms \(25z^4y^6\), \(45zx^2\), and \(-20z\). The GCF of the coefficients 25, 45, -20 is 5, and the GCF of the variable parts is \(z\) (since \(z\) is the lowest power of \(z\) present). So the GCF is \(5z\).

Step2: Factor out the GCF

Factor out \(5z\) from each term:
\(5z(5z^3y^6 + 9x^2 - 4)\)

Now problem 12: \(56h^4j^4k - 48h^3j^4 + 8h^2j^3k\)

Step1: Identify the GCF

The GCF of coefficients 56, 48, 8 is 8. For variables, the lowest power of \(h\) is \(h^2\), lowest power of \(j\) is \(j^3\), and \(k\) is present in two terms but we take the common part. So GCF is \(8h^2j^3\).

Step2: Factor out the GCF

\(8h^2j^3(7h^2jk - 6hj + k)\)

Problem 13: \(28xy^5z^8 + 7x^6y^3z^2 + 56x^3y^3z^3\)

Step1: Identify the GCF

GCF of coefficients 28, 7, 56 is 7. For variables, lowest power of \(x\) is \(x\), lowest power of \(y\) is \(y^3\), lowest power of \(z\) is \(z^2\). So GCF is \(7xy^3z^2\).

Step2: Factor out the GCF

\(7xy^3z^2(4y^2z^6 + x^5 + 8x^2z)\)

Problem 14: \(35x^4 - 35x^3 - 7yz\)

Step1: Identify the GCF

GCF of coefficients 35, 35, 7 is 7. There is no common variable part. So GCF is 7.

Step2: Factor out the GCF

\(7(5x^4 - 5x^3 - yz)\)

Answer:

1. \(5z(5z^3y^6 + 9x^2 - 4)\)
2. \(8h^2j^3(7h^2jk - 6hj + k)\)
3. \(7xy^3z^2(4y^2z^6 + x^5 + 8x^2z)\)
4. \(7(5x^4 - 5x^3 - yz)\)