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

How to find the missing values ?! I never did this.-example-1
User Stussa
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4 votes

Answer:

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

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.

_____

Alternate solution

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)

User Nestor Sokil
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