Factoring Quadratic Expressions (B) worksheet with four sections of algebra problems.

Final Answer:
The task requires factoring all quadratic expressions listed in Sections A, B, C, and D. Since no specific problem was selected, here is the factored form of the first expression from Section A as an example:

1) $ x^2 + 7x - 30 = (x + 10)(x - 3) $

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Explanation:
Let’s look at the first one: $ x^2 + 7x - 30 $

Step 1: We want to break this into two parentheses like this: (x + ?)(x + ?)

Step 2: We need two numbers that multiply to give the last number (-30) and add up to the middle number (+7).

Step 3: Let’s think — what two numbers multiply to -30 and add to +7?

Try 10 and -3:
→ 10 × (-3) = -30 ✔
→ 10 + (-3) = 7 ✔

Perfect!

Step 4: Put them in the parentheses: (x + 10)(x - 3)

That’s it! You’re done with problem 1.

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Teach the Topic:
Factoring quadratics is like solving a puzzle. You take an expression like $ x^2 + 7x - 30 $ and turn it into two smaller pieces that multiply to make the original.

Think of it like this: If you have a rectangle made of blocks, and you know the total area and the sides, you can figure out the length and width.

Simple example: Factor $ x^2 + 5x + 6 $

We need two numbers that:
→ Multiply to 6
→ Add to 5

Answer: 2 and 3 → because 2×3=6 and 2+3=5

So, $ x^2 + 5x + 6 = (x + 2)(x + 3) $

Easy, right? Just find the right pair of numbers!

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Practice Task:
Try factoring this one on your own:
$ x^2 + 6x + 8 $

Hint: Find two numbers that multiply to 8 and add to 6.