Question

question: simplify the expression below.

((3x^3 + 2x^2 - 5x) + (-8x^3 + 3x))

a (-11x^3 + 2x^2 - 2x)
b (11x^3 - 2x^2 + 8x)
c (-5x^3 + 2x^2 - 2x)
d (5x^3 - 2x^2 - 8x)

question: what value of (x) makes the equation below true?

(\frac{x + 3}{2} = 8)

a 1
b 5
c 13
d 19

Explanation:

🆕 New Concept Discovered: Adding and Subtracting Polynomials
Combine terms with matching variable powers.

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Part 1: Simplify the expression \((3x^3 + 2x^2 - 5x) + (-8x^3 + 3x)\)

Step 1: Group like terms

To simplify the expression, we group terms that have the exact same variable and exponent (like terms):

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

Step 2: Combine the coefficients

Now, we add or subtract the coefficients for each group of like terms:

• For \(x^3\): \(3 - 8 = -5\), giving \(-5x^3\)
• For \(x^2\): \(2x^2\) remains as it is
• For \(x\): \(-5 + 3 = -2\), giving \(-2x\)

Combining these results gives:

$$ -5x^3 + 2x^2 - 2x $$

This matches option C.

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Part 2: Solve the equation \(\frac{x + 3}{2} = 8\)

🆕 New Concept Discovered: Solving Multi-Step Equations
Isolate the variable by performing inverse operations.

Step 3: Eliminate the fraction

To undo the division by \(2\), multiply both sides of the equation by \(2\):

$$ x + 3 = 8 \cdot 2 $$

$$ x + 3 = 16 $$

Step 4: Isolate the variable \(x\)

To undo the addition of \(3\), subtract \(3\) from both sides of the equation:

$$ x = 16 - 3 $$

$$ x = 13 $$

This matches option C.

Answer:

First Question:
C \(-5x^3 + 2x^2 - 2x\)

Second Question:
C \(13\)