Question

1. simplify the following polynomials.

a) \\((3x^2 + 6x - 8) + (-5x^2 - x + 4)\\)
b) \\((-6x^2 + 5x + 1) - \\)

Explanation:

Identify the expressions

The image shows two polynomial simplification problems under question 5:
a) \((3x^2 + 6x - 8) + (-5x^2 - x + 4)\)
b) \((-6x^2 + 5x + 1) - (-3x^2 + 2x - 7)\) (partially cut off, but standard subtraction structure is visible as \((-6x^2 + 5x + 1) - (-3x^2 + 2x - 7)\) or similar; let's reconstruct the visible part: \((-6x^2 + 5x + 1) - (\dots)\). Looking closely at the cut-off part, it shows \((-6x^2 + 5x + 1) - (\dots)\). Since the second part of (b) is cut off, we will solve part (a) completely and provide the method for part (b) based on what is visible, or focus primarily on the fully visible part (a).)
Let's re-examine the image. The image is rotated 90 degrees counterclockwise.
Let's read it rotated:
"5. Simplify the following polynomials.
a) \((3x^2 + 6x - 8) + (-5x^2 - x + 4)\)
b) \((-6x^2 + 5x + 1) - (\dots)\)"
Since part (b) is cut off at the end, we will solve part (a) fully.

Remove parentheses for addition

Using the Integer Arithmetic knowledge point, we rewrite the addition without parentheses:

$$ 3x^2 + 6x - 8 - 5x^2 - x + 4 $$

Group like terms

Group the terms with the same variable powers:

$$ (3x^2 - 5x^2) + (6x - x) + (-8 + 4) $$

Combine coefficients

Simplify each grouped set of terms:

$$ -2x^2 + 5x - 4 $$

Answer:

Question 5a

$$-2x^2 + 5x - 4$$