Question

bellringer
multiply the following
polynomials

1. $(x^3 + 4x^2 + 2)(x^2 + 3x)$
2. $(x^2 + 4x)(-x^3 + 5)$

Explanation:

Problem 1: \((x^3 + 4x^2 + 2)(x^2 + 3x)\)

Step 1: Distribute each term

Use the distributive property (FOIL for polynomials) to multiply each term in the first polynomial by each term in the second polynomial.

$$
LATEXBLOCK0
$$

Step 2: Simplify each product

Simplify each term using the rule of exponents \(a^m \cdot a^n = a^{m + n}\).

$$
LATEXBLOCK1
$$

Step 3: Combine like terms

Combine the terms with the same exponent.

$$
LATEXBLOCK2
$$

Problem 2: \((x^2 + 4x)(-x^3 + 5)\)

Step 1: Distribute each term

Use the distributive property to multiply each term in the first polynomial by each term in the second polynomial.

$$
LATEXBLOCK0
$$

Step 2: Simplify each product

Simplify each term using the rule of exponents \(a^m \cdot a^n = a^{m + n}\).

$$
LATEXBLOCK1
$$

Step 3: Rearrange terms

Rearrange the terms in descending order of exponents.

$$
LATEXBLOCK2
$$

Answer:

s:

1. \(x^5 + 7x^4 + 12x^3 + 2x^2 + 6x\)
2. \(-x^5 - 4x^4 + 5x^2 + 20x\)