Answer:
Option (a) is correct.
The factored form of given expression [tex]x^3+6x^2-4x-24[/tex] is [tex](x+6)(x+2)(x-2)[/tex]
Step-by-step explanation:
Given expression [tex]x^3+6x^2-4x-24[/tex]
We have to factorize the given expression completely.
Consider the given expression [tex]x^3+6x^2-4x-24[/tex]
We will solve the given expression by grouping terms and taking common factor common.
[tex]x^3+6x^2-4x-24[/tex]
Taking [tex]x^2[/tex] common from first two terms and -4 common from last two terms, we have,
[tex]x^2(x+6)-4(x+6)[/tex]
Taking (x+6) common , we have,
[tex]x^2(x+6)-4(x+6)=(x+6)(x^2-4)[/tex]
Also , using algebraic identity [tex]a^2-b^2=(a+b)(a-b)[/tex]
We have a = x , b = 2
We have,
[tex]x^2(x+6)-4(x+6)=(x+6)(x^2-4)[/tex]
[tex]\Rightarrow (x+6)(x^2-4)=(x+6)(x+2)(x-2)[/tex]
Thus, the factored form of given expression [tex]x^3+6x^2-4x-24[/tex] is [tex](x+6)(x+2)(x-2)[/tex]
