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a polynomial has been factored below, but some constants are missing. 2x^3-2x^2-24x=ax(x+b)(x+c) what are the missing values of a,b, and c?

User Jahnold
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2 Answers

6 votes

Final answer:

The missing values in the factored polynomial expression are found by matching coefficients and solving a system of equations. The first step reveals that a is 2, and then by comparing coefficients of x^2 and x, a system of equations is established to find b and c.

Step-by-step explanation:

To find the missing values of a, b, and c in the factored polynomial 2x^3-2x^2-24x=ax(x+b)(x+c), we can compare the given polynomial to the factored form and match coefficients.

First, notice that the polynomial is already factored on the right-hand side of the equation. Since the leading term on the left side is 2x^3, the value of a must be 2 to match the leading coefficient. Next, we can expand the right side to get 2x^3 + (2b + 2c)x^2 + 2bcx. Comparing this with the original polynomial, 2x^3 - 2x^2 - 24x, we can set up equations based on the coefficients of x^2 and x:

  • For x^2: 2b + 2c = -2
  • For x: 2bc = -24

To find b and c, we solve this system of equations. Dividing the first equation by 2 gives us b + c = -1. Now, you can plug this into the second equation, assuming b multiplied by c equals -12 (after dividing by 2). By solving these equations, you will find the values of b and c.

User TerenceJackson
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9.0k points
6 votes

Answer:

a=2, b= 3, c=-4

Step-by-step explanation:

The above answer has b and c switched.

Just tested and got it correct

User Bobtune
by
7.5k points
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