Let's simplify the expression Polynomial 1 - Polynomial 2 step by step.

We are given:

• Polynomial 1: $7x^2 - 9x - 2$
• Polynomial 2: $-2x^2 - x + 11$

To subtract Polynomial 2 from Polynomial 1, we distribute the negative sign across Polynomial 2:

$(7x^2 - 9x - 2) - (-2x^2 - x + 11)$

This simplifies to:

$7x^2 - 9x - 2 + 2x^2 + x - 11$

Now, combine like terms:

• $7x^2 + 2x^2 = 9x^2$
• $-9x + x = -8x$
• $-2 - 11 = -13$

Thus, the simplified expression in standard form is:

$9x^2 - 8x - 13$

Do you have any questions or would you like a deeper explanation on any part?

Here are 5 related questions for practice:

1. How would you subtract polynomials that have more than three terms?
2. What happens when you add polynomials instead of subtracting them?
3. How do you factor the resulting polynomial $9x^2 - 8x - 13$?
4. Can you find the roots of the polynomial $9x^2 - 8x - 13$ using the quadratic formula?
5. How do you multiply two polynomials, such as $(7x - 2)(x + 3)$?

Tip: When subtracting polynomials, remember to distribute the negative sign across all terms of the second polynomial before combining like terms.