Question

Three polynomials are factored below, but some coefficients and constants are missing. All of the missing values of a, b, c, and d are integers.

1. x2 - 6x + 8 = (ax + b)(cx + d)

2.3x3 - 6x2 - 24x = 3x(ax + b)(cx + d)

3. 2x2 - 2x - 24 = (ax + b)(cx + d)
Fill in the table with the missing values of a, b, c, and d.

Answer 1

9514 1404 393

Answer:

1. (a, b, c, d) = (1, -4, 1, -2)
2. (a, b, c, d) = (1, -4, 1, 2)
3. (a, b, c, d) = (1, -4, 2, 6)

Explanation:

Once you remove the common factor from the terms, you are looking for factors of the remaining constant term that have a sum equal to the coefficient of the linear term. These factors are the constants in the binomial factors.

__

1. 8 = (-4)(-2) ⇒ x^2 -6x +8 = (x -4)(x -2)

(a, b, c, d) = (1, -4, 1, -2)

__

2. -8 = (-4)(+2) ⇒ 3x^3 -6x^2 -24x = 3x(x -4)(x +2)

(a, b, c, d) = (1, -4, 1, 2)

__

3. -12 = (-4)(3) ⇒ 2x^2 -2x -24 = 2(x -4)(x +3) = (x -4)(2x +6)

(a, b, c, d) = (1, -4, 2, 6) or (2, -8, 1, 3)