To factor the quadratic expression \( 7x^2 - 4x - 3 \), follow these steps:

### Step 1: Multiply the coefficient of \( x^2 \) (which is 7) by the constant term (which is -3). 
\[
7 \times (-3) = -21
\]

### Step 2: Find two numbers that multiply to give -21 and add up to the middle term's coefficient, which is -4.
The two numbers are -7 and 3 because:
\[
-7 \times 3 = -21 \quad \text{and} \quad -7 + 3 = -4
\]

### Step 3: Rewrite the middle term (-4x) using -7 and 3.
\[
7x^2 - 7x + 3x - 3
\]

### Step 4: Factor by grouping. Group the terms in pairs:
\[
(7x^2 - 7x) + (3x - 3)
\]

### Step 5: Factor out the greatest common factor (GCF) from each group:
\[
7x(x - 1) + 3(x - 1)
\]

### Step 6: Factor out the common binomial factor \((x - 1)\):
\[
(7x + 3)(x - 1)
\]

So, the factored form of \( 7x^2 - 4x - 3 \) is:
\[
(7x + 3)(x - 1)
\]

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How do you factor a quadratic expression when the leading coefficient is 1?
2. Can you factor \( 8x^2 + 2x - 3 \) using the same method?
3. What is the significance of factoring in solving quadratic equations?
4. How do you solve a quadratic equation using its factored form?
5. Can you complete the square for the expression \( 7x^2 - 4x - 3 \)?

**Tip:** Always check your factored form by expanding it to ensure you get the original expression!

Learn how to factor the quadratic expression 7x^2 - 4x - 3 step by step. This solution demonstrates factoring by grouping and finding the greatest common factor, suitable for students in Grades 9-11. Explore key algebraic concepts and solve similar problems efficiently.

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