Question

The product of 2x – 3 and x + 4 can be expressed as:

A) 2x² + 5x - 12
B) 3x + 1
C) 2x² + x - 12
D) 2x² – 12

Please select the correct answer.""

Answer 1

The product of the binomials 2x - 3 and x + 4 is determined by multiplying each term of the first binomial by each term of the second, resulting in the expression 2x² + 5x - 12.

Step-by-step explanation:

The product of 2x - 3 and x + 4 can be found by using the distributive property (also known as the FOIL method in this case), where we multiply each term of the first polynomial by each term of the second polynomial. The steps are as follows:

1. Multiply the first terms: 2x × x = 2x².
2. Multiply the outside terms: 2x × 4 = 8x.
3. Multiply the inside terms: -3 × x = -3x.
4. Multiply the last terms: -3 × 4 = -12.
5. Add up the products: 2x² + 8x - 3x - 12, which simplifies to 2x² + 5x - 12.

Hence, the correct answer is A) 2x² + 5x - 12.