Answered

Factor completely. x 3 + 6x 2 - 4x - 24

a.(x + 6)(x - 2)(x + 2)

b.(x + 2)(x - 6)(x + 2)

c.(x - 6)(x + 2)(x + 2)x^3 + 6x^2 - 4x - 24 = x^2(x + 6) - 4(x + 6) = (x + 6)(x^2 - 4) = (x + 6)(x + 2)(x - 2)

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Answer:

Option (a) is correct.

The factored form of given expression \(x^3+6x^2-4x-24\) is \((x+6)(x+2)(x-2)\)

Step-by-step explanation:

  Given  expression \(x^3+6x^2-4x-24\)

We have to factorize the given expression completely.

Consider the given expression \(x^3+6x^2-4x-24\)

We will solve the given expression by grouping terms and taking common factor common.

\(x^3+6x^2-4x-24\)

Taking \(x^2\) common from first two terms and  -4 common from last two terms, we have,

\(x^2(x+6)-4(x+6)\)

Taking (x+6) common , we have,

\(x^2(x+6)-4(x+6)=(x+6)(x^2-4)\)

Also , using algebraic identity \(a^2-b^2=(a+b)(a-b)\)

We have a = x , b = 2

We have,

\(x^2(x+6)-4(x+6)=(x+6)(x^2-4)\)

\(\Rightarrow (x+6)(x^2-4)=(x+6)(x+2)(x-2)\)

Thus, the factored form of given expression \(x^3+6x^2-4x-24\) is \((x+6)(x+2)(x-2)\)

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