To find the missing values of a, b, and c, we can expand the right side of the equation and compare it to the given polynomial.
Expanding the right side:
ax(x+b)(x+c) = ax(x^2 + cx + bx + bc)
= ax^3 + acx^2 + abx^2 + abc
Setting this equal to the given polynomial:
2x^3 - 8x^2 - 24x = ax^3 + acx^2 + abx^2 + abc
Now we can compare coefficients to find the values of a, b, and c.
For the x^3 term:
2 = a, so a = 2
For the x^2 term:
-8 = ac + ab
-8 = 2c + 2b
c + b = -4
For the x term:
-24 = abc
Since a = 2, bc = -12
We need to find two numbers b and c whose product is -12 and whose sum is -4.
The factors of -12 that add up to -4 are -6 and 2, so b = -6 and c = 2.
Therefore, the missing values of a, b, and c are 2, -6, and 2.
A polynomial has been factored below, but some constants are missing.
2x^3-8x^2-24x=ax(x+b)(x+c)
What are the missing values of a, b, and c?
1 answer