https://file.aiquickdraw.com/mathbot/file/1727190860493ovjp1v5i.jpg

The problem given in the image asks to factorize the quadratic expression:

\[
6x^2 + 11x - 10
\]

Let's go step by step to factorize it.

### Step 1: Multiply the coefficient of \(x^2\) (which is 6) by the constant term (which is -10).
\[
6 \times (-10) = -60
\]

### Step 2: Find two numbers that multiply to give -60 and add up to the middle term’s coefficient, which is 11.
The numbers are 15 and -4 because:
\[
15 \times (-4) = -60 \quad \text{and} \quad 15 + (-4) = 11
\]

### Step 3: Rewrite the middle term (11x) as a sum of 15x and -4x.
\[
6x^2 + 15x - 4x - 10
\]

### Step 4: Group the terms in pairs.
\[
(6x^2 + 15x) - (4x + 10)
\]

### Step 5: Factor out the greatest common factor (GCF) from each group.
\[
3x(2x + 5) - 2(2x + 5)
\]

### Step 6: Factor out the common binomial factor \((2x + 5)\).
\[
(3x - 2)(2x + 5)
\]

Thus, the factorization of \(6x^2 + 11x - 10\) is:

\[
(3x - 2)(2x + 5)
\]

Would you like more details or have any further questions? Here are five related questions you might explore:

1. How do you factorize quadratics with complex solutions?
2. What methods can be used to check if a factorization is correct?
3. How do you solve a quadratic equation after factorization?
4. How does the discriminant of a quadratic relate to factorization?
5. What are some examples of quadratics that cannot be factored with real numbers?

**Tip:** Always check your factorization by expanding the factors to ensure they give the original quadratic expression.

Learn how to factorize the quadratic expression 6x^2 + 11x - 10 step by step. This example covers algebraic concepts such as factoring quadratic expressions and the zero product property. Suitable for students in Grades 9-10.

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