Questions: Multiply the polynomial by the monomial using the distributive property and/or the product rule of exponents. [ (-2)left(-4 x^2+2 x-3right) ]

Solution Steps

We multiply the monomial \(a \cdot x^n\) by each term of the polynomial \(\sum_{i=0}^{m} b_i \cdot x^i\), where \(a = -2\), \(n = 0\), and the polynomial coefficients \(b_i\) are [-4, 2, -3].

When multiplying \(x^n\) by \(x^i\), we add the exponents to get \(x^{n+i}\).

The resulting polynomial after multiplication is: \(\sum_{i=0}^{m} (-2 \cdot b_i) \cdot x^{n+i}\), which simplifies to: 8_x^0 - 4_x^1 + 6*x^2.

Final Answer: