https://file.aiquickdraw.com/mathbot/file/1728479460338dgc6ubrn.jpg

The given expression to factor is:

\[
4x^2 - 3x - 10
\]

The partially factored form provided is:

\[
(4x + ?)(x - \text{[blank]})
\]

Let's factor the quadratic expression step by step.

### Step 1: Multiply the leading coefficient (4) by the constant (-10)
This gives:
\[
4 \times (-10) = -40
\]

### Step 2: Find two numbers that multiply to -40 and add up to the middle term coefficient (-3)
The numbers are **-8** and **5** because:
\[
-8 \times 5 = -40
\quad \text{and} \quad
-8 + 5 = -3
\]

### Step 3: Rewrite the middle term using -8 and 5
\[
4x^2 - 8x + 5x - 10
\]

### Step 4: Group terms and factor by grouping
\[
(4x^2 - 8x) + (5x - 10)
\]
Factor out the greatest common factor (GCF) from each group:
\[
4x(x - 2) + 5(x - 2)
\]

### Step 5: Factor out the common binomial
\[
(4x + 5)(x - 2)
\]

### Final Answer:
\[
(4x + 5)(x - 2)
\]

So, the missing terms are **5** and **2**, and the factored form is:
\[
(4x + 5)(x - 2)
\]

Would you like further details or have any questions?

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Here are 5 related questions:
1. How do you factor quadratic expressions with a leading coefficient greater than 1?
2. What is the "factoring by grouping" method, and how does it work?
3. How can you check if a factored form is correct?
4. What if the discriminant (b² - 4ac) is negative—what does that mean for factoring?
5. How does factoring help in solving quadratic equations?

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

Factor 4x^2 - 3x - 10. Fill in the missing terms in the partially factored form: (4x + ?) (x - [blank]).

Learn how to factor the quadratic expression 4x^2 - 3x - 10 using factoring by grouping. This step-by-step guide covers key concepts and techniques suitable for students in Grades 9-10.

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