Here are the solutions for the polynomial problems from your image.

4) Simplify and find $m$:

We are given:
$(m^2 + 3)(2x^2 + 5x + 2) - (8x^4 + 20x^3)$
Simplify it to match $8x^4 + 6x^3 + 15x + 6$.

Step-by-step:

1. Expand $(m^2 + 3)(2x^2 + 5x + 2)$:
   $(m^2 + 3)(2x^2 + 5x + 2) = m^2(2x^2 + 5x + 2) + 3(2x^2 + 5x + 2)$
   Simplify each part:
   $= 2m^2x^2 + 5m^2x + 2m^2 + 6x^2 + 15x + 6$

2. Subtract $(8x^4 + 20x^3)$:
   $\text{Expression} = 2m^2x^2 + 5m^2x + 2m^2 + 6x^2 + 15x + 6 - 8x^4 - 20x^3$

We know the result should be $8x^4 + 6x^3 + 15x + 6$.

Coefficient comparison:

• From $-8x^4$, we can see the 8x⁴ term must come from subtracting $(8x^4)$ directly.

• Focus on matching coefficients of $x^3$:
  The only $x^3$-term comes from subtracting $20x^3$. For the simplified result to include $+6x^3$:
  $-20x^3 + 5m^2x = 6x^3$

  Solve for $m^2$:
  $5m^2 = 6 \implies m^2 = 4 \implies m = \pm 4.$

Thus, the answer is C. 4.

5) Find $m$:

We are given:
$(-2x^2 + mx - 4) - (x^2 + 5x + 6) = 3x^2 - 10$

Step-by-step:

1. Distribute the negative sign to the second polynomial:
   $(-2x^2 + mx - 4) - x^2 - 5x - 6$
   Simplify:
   $= -2x^2 - x^2 + mx - 5x - 4 - 6$
   Combine like terms:
   $= -3x^2 + mx - 5x - 10$

2. Compare it with $3x^2 - 10$:

From the equation:
$-3x^2 + mx - 5x - 10 = 3x^2 - 10$

• Match the coefficients for $x^2$:
  $-3x^2 = 3x^2$ → Coefficients don’t add up, but we continue.