Question

1. $14x^3 + 18x + 8$
2. $10x^2y^4 + 30xy$

Explanation:

Problem 7: \(14x^3 + 18x + 8\)

Step 1: Find the GCF of coefficients

The coefficients are 14, 18, 8. The GCF of 14, 18, 8 is 2.

Step 2: Factor out the GCF

Factor out 2 from each term: \(2(7x^3 + 9x + 4)\) (Note: The cubic polynomial \(7x^3 + 9x + 4\) doesn't factor further with real coefficients easily, so this is the factored form for now.)

Problem 9: \(10x^2y^4 + 30xy\)

Step 1: Find GCF of coefficients and variables

• Coefficients: GCF of 10 and 30 is 10.
• Variables: For \(x\), the lowest power is \(x^1\) (from \(30xy\)); for \(y\), the lowest power is \(y^1\) (from \(30xy\)). So the GCF of variables is \(xy\).
• Overall GCF: \(10xy\)

Step 2: Factor out the GCF

Factor out \(10xy\) from each term: \(10xy(xy^3 + 3)\)

Answer:

s:

1. \(\boldsymbol{2(7x^3 + 9x + 4)}\)
2. \(\boldsymbol{10xy(xy^3 + 3)}\)