Question

Which of the following is the product of (3x² - 1)(x² - 4)?

a) 3x⁴ - 13x² + 4
b) 3x⁴ - 13x² - 4
c) 3x⁴ + 13x² - 4
d) 3x⁴ + 13x² + 4

Answer 1

To find the product of (3x² - 1)(x² - 4), we multiply each term of the first polynomial by each term of the second polynomial and combine like terms, resulting in 3x⁴ - 13x² + 4.

Step-by-step explanation:

The product of the polynomials (3x² - 1)(x² - 4) requires us to use the distributive property, also known as the FOIL method, to multiply each term in the first polynomial by each term in the second polynomial. Here is how it's done step-by-step:

• Multiply the first terms: 3x² * x² = 3x⁴.
• Multiply the outer terms: 3x² * (-4) = -12x².
• Multiply the inner terms: -1 * x² = -x².
• Multiply the last terms: -1 * (-4) = 4.

Combine like terms (the x² terms in this case):

-12x² - x² = -13x².

So, the product of the two polynomials is 3x⁴ - 13x² + 4, which corresponds to option a).