Consider the polynomial expression provided below: (2x - 3)(x + 4) - 2(x^2 - 5x + 1) Which… — Armed Services Vocational Aptitude Battery (ASVAB)

Consider the polynomial expression provided below:

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

Which of the following represents its fully simplified equivalent?

The completely simplified equivalent expression is

15x - 14

The expression correctly expands to

2x^2 + 5x - 12

on the left and

-2x^2 + 10x - 2

on the right. When adding these together, the

x^2

terms cancel out, the

x

terms sum to

15x

, and the constants sum to

-14

, leaving

15x - 14

Expand

(2x - 3)(x + 4)

using the distributive property.

2x^2 + 8x - 3x - 12

, which simplifies to

2x^2 + 5x - 12

To eliminate the first set of parentheses by multiplying each term in the first binomial by each term in the second binomial.

Distribute

-2

to each term inside the trinomial

(x^2 - 5x + 1)

-2x^2 + 10x - 2

To eliminate the second set of parentheses, carefully applying the negative sign to all inner terms.

Combine the expanded expressions.

(2x^2 + 5x - 12) + (-2x^2 + 10x - 2)

To prepare the entire expression for the collection of like terms.

Group and combine like terms (

x^2

terms,

x

terms, and constants).

(2x^2 - 2x^2) + (5x + 10x) + (-12 - 2) = 0x^2 + 15x - 14 = 15x - 14

To achieve the final simplified standard form.

Expanding polynomials, distributing negative coefficients, and combining like terms.

Question