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Burka [1]
3 years ago
11

How to find the missing values ?! I never did this.

Mathematics
1 answer:
Semmy [17]3 years ago
8 0

Answer:

  (a, b, c) = (2, -6, 2)  or  (2, 2, -6)

Step-by-step explanation:

Expand the expression on the right and match coefficients, or factor the expression on the left and match factors.

  2x³ -8x² -24x = ax(x +b)(x +c)

  2x(x² -4x -12) = ax(x +b)(x +c)

  2x(x -6)(x +2) = ax(x +b)(x +c)

In this form, we can match the numbers to get ...

  • a = 2
  • b = -6
  • c = 2

You may recognize that b and c can be interchanged.

_____

<em>Alternate solution</em>

If you expand the expression on the right, you get ...

  = ax³ +a(b+c)x² +abcx

This gives you 3 equations:

  • a = 2
  • 2(b +c) = -8
  • 2bc = -24

This is basically the same factoring problem in another form. You have ...

  bc = -12

  b+c = -4

The factors of -12 are ...

  -12 = 1(-12) = 2(-6) = 3(-4) . . . . . . with sums -11, -4, -1

So, b and c are -6 and 2, in no particular order.

  (a, b, c) = (2, -6, 2)  or  (2, 2, -6)

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