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 + 2x - 15 = (ax + b)(cx + d)
2. 2x³ + 6x² - 20x = 2x(ax + b)(cx + d)
3. 9x² +21x + 6 = (ax + b)(cx + d)
Fill in the table with the missing values of a, b, c, and d

Answer 1

To fill in the table with the missing values of a, b, c, and d in the given expressions, you need to factor the expressions based on the given factorization format and find the missing values of a, b, c, and d.

Step-by-step explanation:

To fill in the table with the missing values of a, b, c, and d in the given expressions:

1. To factor the expression x² + 2x - 15 = (ax + b)(cx + d), we need to find two numbers that multiply to give -15 and add to give 2. The numbers are 5 and -3. So, a = 1, b = 5, c = 1, and d = -3.
2. To factor the expression 2x³ + 6x² - 20x = 2x(ax + b)(cx + d), we can first factor out the common factor of 2x to get 2x(x² + 3x - 10) = 2x(ax + b)(cx + d). We need to find two numbers that multiply to give -10 and add to give 3. The numbers are 5 and -2. So, a = 1, b = 5, c = 1, and d = -2.
3. To factor the expression 9x² + 21x + 6 = (ax + b)(cx + d), we need to find two numbers that multiply to give 6 and add to give 21. The numbers are 3 and 2. So, a = 3, b = 3, c = 3, and d = 2.