Question

multiply the polynomials.
(7x² + 5x + 7)(4x - 6)
a. 28x³ - 22x² - 2x + 42
b. 28x³ - 62x² - 2x - 42
c. 28x³ - 22x² - 58x - 42
d. 28x³ - 22x² - 2x - 42

Explanation:

Step1: Apply distributive property

Multiply each term in the first polynomial by each term in the second polynomial:
$$(7x^2)(4x) + (7x^2)(-6) + (5x)(4x) + (5x)(-6) + 7(4x) + 7(-6)$$

Step2: Simplify each product

Calculate each term:
$$28x^3 - 42x^2 + 20x^2 - 30x + 28x - 42$$

Step3: Combine like terms

Combine the \(x^2\) terms and \(x\) terms:

• For \(x^2\): \(-42x^2 + 20x^2 = -22x^2\)
• For \(x\): \(-30x + 28x = -2x\)

So the simplified polynomial is:
$$28x^3 - 22x^2 - 2x - 42$$

Answer:

D. \(28x^3 - 22x^2 - 2x - 42\)