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.

Question

1. x^2 + 2x - 8 = (ax + b)(cx + d)

2. 2x^3 + 2x^2 - 24x = 2x(ax + b)(cx + d)

3. 6x^2 - 15x - 9 = 3(ax + b)(cx +d)

Fill in the table with the missing values of a, b, c, and d.



	a	b	c	d
1.	1	-2	1
2.	1			4
3.		1	1	-3

Answer 1

1. x² + 2x - 8 = (x-2)(x+4)

Thus, a = 1, b = -2, c = 1, and d = 4.

2. 2x³ + 2x² - 24x = 2x(x²+x-12) = 2x(x-3)(x+4)

Thus, a = 1, b = -3, c = 1, and d = 4.

3. 6x² - 15x - 9 = 3(2x²-5x-3) = 3(2x+1)(x-3)

Thus, a = 2, b = 1, c = 1, and d = -3.