Subtract minus, 10, x, plus, 3−10x+3 from minus, 7, x, squared, plus, 5, x, plus, 10−7x
2
+5x+10.

To subtract the expression \(-10x + 3\) from \(-7x^2 + 5x + 10\), follow these steps:

### Step 1: Write down the two expressions clearly:
1. First expression: \(-7x^2 + 5x + 10\)
2. Second expression (which you are subtracting): \(-10x + 3\)

### Step 2: Subtract the second expression from the first.
This means you need to subtract every term in \(-10x + 3\) from \(-7x^2 + 5x + 10\). Here's how it works:

\[
(-7x^2 + 5x + 10) - (-10x + 3)
\]

Distribute the negative sign over the second expression:

\[
= -7x^2 + 5x + 10 + 10x - 3
\]

### Step 3: Combine like terms.
Now, combine the terms with the same powers of \(x\):

\[
= -7x^2 + (5x + 10x) + (10 - 3)
\]

\[
= -7x^2 + 15x + 7
\]

### Final Answer:
\[
-7x^2 + 15x + 7
\]

Would you like more details or further explanation?

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Here are 5 related questions to expand your understanding:
1. How do you subtract polynomials with more variables?
2. What happens when you subtract polynomials involving fractional coefficients?
3. How can you factor the resulting polynomial \( -7x^2 + 15x + 7 \)?
4. How do you perform subtraction on polynomials of different degrees?
5. What is the importance of combining like terms in polynomial operations?

**Tip:** Always distribute the negative sign carefully when subtracting polynomials to avoid errors.

Explore how to subtract the polynomial -10x + 3 from -7x^2 + 5x + 10 using distributive property and combining like terms. This step-by-step solution simplifies the expression to -7x^2 + 15x + 7. Ideal for students in Grades 8-10 learning polynomial operations.

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