Which expression is a factor of 10x2 + 11x + 3?

x − 3
2x + 1
5x − 3
10x + 3

To find which expression is a factor of \( 10x^2 + 11x + 3 \), we can use factoring or the Remainder Theorem. Let's solve it by factoring the given quadratic expression.

1. **Check the factors:**

We need to factor \( 10x^2 + 11x + 3 \). We look for two numbers whose product is \( 10 \times 3 = 30 \) and whose sum is \( 11 \).

These numbers are 5 and 6.

2. **Rewrite the middle term:**

We can rewrite the quadratic as:
\[
10x^2 + 5x + 6x + 3
\]

3. **Factor by grouping:**

Group the terms as follows:
\[
(10x^2 + 5x) + (6x + 3)
\]

Factor out the common factors in each group:
\[
5x(2x + 1) + 3(2x + 1)
\]

Now we can factor out \( (2x + 1) \):
\[
(5x + 3)(2x + 1)
\]

4. **Identify the factors:**

The factors are \( 5x + 3 \) and \( 2x + 1 \).

So, the correct options are:

- **2x + 1**
- **5x − 3** (after correcting the sign, should be +3)

The factor from the options given is:

**2x + 1.**

Would you like more details on the factoring process or have any other questions?

### Relative Questions:
1. How do you determine if a polynomial is factorable?
2. What is the Remainder Theorem and how does it help in factoring?
3. Can you use synthetic division to factor quadratics?
4. What are the general steps to factor any quadratic polynomial?
5. How can you verify that the factorization of a polynomial is correct?

### Tip:
Always double-check the signs and coefficients when factoring, as small mistakes can lead to incorrect factors.

Which expression is a factor of 10x^2 + 11x + 3? x − 3, 2x + 1, 5x − 3, 10x + 3

Discover how to factor the quadratic equation 10x^2 + 11x + 3 using the product-sum method. Learn the step-by-step solution with a detailed explanation of the process and identify the correct factor from the options. Suitable for students in Grades 8-10.

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