Question

simplify the following expression.\\((5x^2 - 3x + 2)(x - 6)\\)\\(?x^3 + \square x^2 + \square x + \square\\)

Explanation:

Step1: Distribute \(5x^2\)

Multiply \(5x^2\) by each term in \((x - 6)\):
\(5x^2 \cdot x = 5x^3\), \(5x^2 \cdot (-6) = -30x^2\)

Step2: Distribute \(-3x\)

Multiply \(-3x\) by each term in \((x - 6)\):
\(-3x \cdot x = -3x^2\), \(-3x \cdot (-6) = 18x\)

Step3: Distribute \(2\)

Multiply \(2\) by each term in \((x - 6)\):
\(2 \cdot x = 2x\), \(2 \cdot (-6) = -12\)

Step4: Combine like terms

• \(x^3\) term: \(5x^3\)
• \(x^2\) terms: \(-30x^2 - 3x^2 = -33x^2\)
• \(x\) terms: \(18x + 2x = 20x\)
• Constant term: \(-12\)

Answer:

The coefficient of \(x^3\) is \(5\), so the first box is \(5\). The full simplified expression is \(5x^3 - 33x^2 + 20x - 12\), so the coefficients are \(5\) (for \(x^3\)), \(-33\) (for \(x^2\)), \(20\) (for \(x\)), and \(-12\) (constant).

For the first box (coefficient of \(x^3\)): \(\boldsymbol{5}\)