Question

Find the product of (2x2 + 423) (3x* - 7x3). Provide your answer in standard form (descending order of exponents).
You will not receive credit without all work shown.

Answer 1

To find the product of the two polynomials \((2x^2 + 423)(3x - 7x^3)\), we will use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial.

Let's break it down:

1. **Multiply the term \(2x^2\) from the first polynomial by each term in the second polynomial:**
- \(2x^2 \cdot 3x = 6x^3\)
- \(2x^2 \cdot (-7x^3) = -14x^5\)

2. **Multiply the constant term \(423\) from the first polynomial by each term in the second polynomial:**
- \(423 \cdot 3x = 1269x\)
- \(423 \cdot (-7x^3) = -2961x^3\)

3. **Now, combine all the products obtained:**
\[
-14x^5 + 6x^3 + 1269x - 2961x^3
\]

4. **Combine like terms:**
- For \(x^3\): \(6x^3 - 2961x^3 = -2955x^3\)

5. **Write the final polynomial in standard form (descending order of exponents):**
\[
-14x^5 - 2955x^3 + 1269x
\]

Thus, the product of \((2x^2 + 423)(3x - 7x^3)\) in standard form is:
\[
\boxed{-14x^5 - 2955x^3 + 1269x}
\]