Question

factor ( 36x^3 - 24x^2 ).

a) ( 3x^2(12x + 8) )
b) ( 4x^2(9x^2 - 6) )
c) ( -6x(6x^2 - 4x) )
d) ( 12x^2(3x - 2) )

Explanation:

Step1: Find GCF of coefficients and variables

The coefficients are 36 and 24. GCF of 36 and 24 is 12. For variables, the lowest power of \(x\) is \(x^2\) (from \(x^2\) in \(24x^2\) and \(x^3\) in \(36x^3\)). So GCF is \(12x^2\).

Step2: Factor out GCF

Factor \(12x^2\) from \(36x^3 - 24x^2\):
\(36x^3 - 24x^2 = 12x^2(3x - 2)\) (since \(12x^2\times3x = 36x^3\) and \(12x^2\times(-2)= -24x^2\)).

Check other options:

• Option A: \(3x^2(12x + 8)=36x^3 + 24x^2\) (sign and terms wrong).
• Option B: \(4x^2(9x^2 - 6)=36x^4 - 24x^2\) (exponent of \(x\) wrong).
• Option C: \(-6x(6x^2 - 4x)= -36x^3 + 24x^2\) (sign and terms wrong).

Answer:

D) \(12x^2(3x - 2)\)