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Let's go through the factoring of each polynomial step by step.

### Question 4
The polynomial is:

\[
x^2 y - 14xy + 48y
\]

First, factor out the common term, which is \( y \):

\[
y(x^2 - 14x + 48)
\]

Now, factor the quadratic expression \( x^2 - 14x + 48 \). We are looking for two numbers that multiply to 48 and add up to -14. These numbers are -6 and -8:

\[
y(x - 6)(x - 8)
\]

So the factored form of the polynomial is:

\[
y(x - 6)(x - 8)
\]

---

### Question 5
The polynomial is:

\[
x^2 y - 9xy + 18y
\]

Again, factor out the common term, which is \( y \):

\[
y(x^2 - 9x + 18)
\]

Now, factor the quadratic expression \( x^2 - 9x + 18 \). We need two numbers that multiply to 18 and add up to -9. These numbers are -3 and -6:

\[
y(x - 3)(x - 6)
\]

So the factored form of the polynomial is:

\[
y(x - 3)(x - 6)
\]

---

### Question 6
The polynomial is:

\[
3x^2 - 42x + 144
\]

First, factor out the greatest common factor (GCF), which is 3:

\[
3(x^2 - 14x + 48)
\]

Now, factor the quadratic expression \( x^2 - 14x + 48 \). Like in Question 4, we are looking for two numbers that multiply to 48 and add up to -14. These numbers are -6 and -8:

\[
3(x - 6)(x - 8)
\]

So the factored form of the polynomial is:

\[
3(x - 6)(x - 8)
\]

---

Would you like further clarification on any of these steps?

Here are 5 related questions for practice:
1. How do you factor polynomials that don’t have a common factor?
2. What is the importance of factoring in solving quadratic equations?
3. How would you factor a trinomial when the leading coefficient is not 1?
4. How do you apply factoring to solve word problems in algebra?
5. Can every polynomial be factored? Why or why not?

**Tip**: Always look for a common factor before factoring a quadratic expression; it can simplify the process significantly.

Factor the following polynomials: 1) x²y - 14xy + 48y, 2) x²y - 9xy + 18y, 3) 3x² - 42x + 144

This lesson focuses on factoring polynomials such as x²y - 14xy + 48y and 3x² - 42x + 144. Learn how to apply the quadratic equation factoring method, find common factors, and factor quadratic expressions. Ideal for students in Grades 8-10.

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