Question

"Multiply (3x + 2)(x 2 - 4x + 1).

a. 3x³ - 10x² - 8x + 2
b. 3x³ + 2x² + 11x + 2
c. 3x³ - 10x² + 11x + 2
d. 3x³ + 2x² - 5x + 2
e. none of the above"

Answer 1

The correct answer to the multiplication of the binomials (3x + 2) and (x² - 4x + 1) is option a, which is 3x³ - 10x² - 8x + 2. This result is obtained by using the FOIL method and combining like terms.

Step-by-step explanation:

To multiply the binomials (3x + 2) and (x² - 4x + 1), we will apply the distributive property, also known as the FOIL method (First, Outer, Inner, Last). We must multiply each term in the first binomial by each term in the second binomial and then combine like terms.

First, multiply the First terms in each binomial: (3x) * (x²) = 3x³.

Next, multiply the Outer terms: (3x) * (-4x) = -12x².

Then multiply the Inner terms: (2) * (x²) = 2x².

Lastly, multiply the Last terms: (2) * (-4x) = -8x and (2) * (1) = 2.

Now, combine like terms: 3x³ - 12x² + 2x² - 8x + 2 = 3x³ - 10x² - 8x + 2.

The correct answer is therefore option a. 3x³ - 10x² - 8x + 2.

Answer 2

e

Step-by-step explanation:

to multiply (3x + 2)(x² - 4x + 1)

each term in the second factor is multiplied by each term in the first factor, that is

3x(x² - 4x + 1) + 2(x² - 4x + 1) ← distribute parenthesis

= 3x³ - 12x² + 3x + 2x² - 8x + 2 ← collect like terms

= 3x³ + (- 12x² + 2x²) + (3x - 8x) + 2

= 3x³ + (- 10x²) + (- 5x) + 2

= 3x³ - 10x² - 5x + 2

this not appear as an option in the given list.