When the expression (5x^2 - 8x + 2) - (2x^2 - 4x - 9) is written in the standard form ax^2… — ACT

When the expression $(5x^2 - 8x + 2) - (2x^2 - 4x - 9)$ is written in the standard form $ax^2 + bx + c$ , where $a$ , $b$ , and $c$ are integers, what is the value of $b$ ?

Answer: -4

Answer

The correct answer is

-4

, which is the coefficient of the

x

term after simplifying the expression.

To subtract polynomials, we distribute the negative sign to all terms of the polynomial being subtracted and then combine like terms. Simplifying

(5x^2 - 8x + 2) - (2x^2 - 4x - 9)

gives

5x^2 - 8x + 2 - 2x^2 + 4x + 9 = 3x^2 - 4x + 11

. Comparing this to

ax^2 + bx + c

shows that

b

, the coefficient of the

x

term, is

-4

Step-by-Step Solution

Distribute the subtraction sign to all terms inside the second set of parentheses.

-2x^2 + 4x + 9

Subtracting a polynomial is equivalent to adding its opposite, which means changing the sign of every term in that polynomial.

Group and combine like terms from both polynomials.

3x^2 - 4x + 11

Like terms (terms with the same variable raised to the same power) can be combined by adding or subtracting their coefficients:

(5x^2 - 2x^2) = 3x^2

(-8x + 4x) = -4x

, and

(2 + 9) = 11

Compare the simplified expression to the standard form

ax^2 + bx + c

to identify the value of

b

b = -4

In the standard form

ax^2 + bx + c

, the coefficient of the

x

term is represented by

b

. In the simplified expression

3x^2 - 4x + 11

, the coefficient of

x

-4

Key Concept

Polynomial Subtraction and Combining Like Terms

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic