Order the steps from first to last that would be used to factor: 3x2−13x−10 (7 points) Arrange responses in the correct order to answer the question. Select a response, navigate to the desired position and insert response at that position. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can be moved using the up and down arrow keys or by dragging with a mouse.

Question

GPT-4o mini · Answer

To factor the quadratic expression $3x^2 - 13x - 10$, you would generally follow these steps: 1. **Identify $a$, $b$, and $c$** in the quadratic $ax^2 + bx + c$. Here, $a = 3$, $b = -13$, and $c = -10$. 2. **Multiply $a$ and $c$**. Calculate $3 \times -10 = -30$. 3. **Find two numbers that multiply to $-30$** (the product from step 2) and add to $-13$ (the value of $b$). The numbers are $-15$ and $2$. 4. **Rewrite the middle term** $-13x$ using the two numbers found in step 3. Rewrite $3x^2 - 15x + 2x - 10$. 5. **Factor by grouping**. Group the first two terms and the last two terms: $(3x^2 - 15x) + (2x - 10)$. 6. **Factor out the common factors from each group**: $3x(x - 5) + 2(x - 5)$. 7. **Factor out the common binomial**: $(x - 5)(3x + 2)$. So, in order, the steps to factor $3x^2 - 13x - 10$ are as follows: 1. Identify $a$, $b$, and $c$. 2. Multiply $a$ and $c$. 3. Find two numbers that multiply to $-30$ and add to $-13$. 4. Rewrite the middle term using those two numbers. 5. Factor by grouping. 6. Factor out the common factors from each group. 7. Factor out the common binomial. If you need to arrange the provided responses according to these steps, please provide those responses and I can help you arrange them correctly!