Question

simplify the following expression.\\((x^2 + 9x - 3)(5x + 1)\\)\\(?x^3 + \square x^2 + \square x + \square\\)

Explanation:

Step1: Use distributive property (FOIL for polynomials)

Multiply each term in the first polynomial by each term in the second polynomial:
\(x^2 \cdot 5x + x^2 \cdot 1 + 9x \cdot 5x + 9x \cdot 1 - 3 \cdot 5x - 3 \cdot 1\)

Step2: Simplify each product

\(5x^3 + x^2 + 45x^2 + 9x - 15x - 3\)

Step3: Combine like terms

For \(x^2\) terms: \(x^2 + 45x^2 = 46x^2\)
For \(x\) terms: \(9x - 15x = -6x\)
So the polynomial is \(5x^3 + 46x^2 - 6x - 3\)

Answer:

The coefficient of \(x^3\) is \(5\), the coefficient of \(x^2\) is \(46\), the coefficient of \(x\) is \(-6\), and the constant term is \(-3\). So filling in the blanks: \(\boldsymbol{5}\) for \(x^3\), \(\boldsymbol{46}\) for \(x^2\), \(\boldsymbol{-6}\) for \(x\), and \(\boldsymbol{-3}\) for the constant term.