Let P(x) = (3x^2 - 2x + 4)(2x - 5) - (4x^3 - 7x^2 + x - 3). When P(x) is simplified and wr… — ACT

Let $P(x) = (3x^2 - 2x + 4)(2x - 5) - (4x^3 - 7x^2 + x - 3)$ . When $P(x)$ is simplified and written in standard form, what is the coefficient of the $x^2$ term?

Answer: -12

Answer

The coefficient of the

x^2

term is -12.

Expanding

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

yields

6x^3 - 19x^2 + 18x - 20

. Distributing the negative sign across the second polynomial yields

-4x^3 + 7x^2 - x + 3

. Combining the

x^2

terms gives

-19x^2 + 7x^2 = -12x^2

, so the coefficient of the

x^2

term is -12.

Step-by-Step Solution

Expand the product of the trinomial and the binomial:

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

6x^3 - 19x^2 + 18x - 20

To find the expanded form of the first polynomial component before subtraction

Distribute the negative sign across the second polynomial:

-(4x^3 - 7x^2 + x - 3)

-4x^3 + 7x^2 - x + 3

To prepare the second polynomial for combination of like terms

Combine the like terms from the two expanded components

2x^3 - 12x^2 + 17x - 17

To write the entire polynomial in standard form and identify the coefficient of

x^2

Key Concept

Operations on Polynomials

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic