Question

question 8 of 10
what is the factorization of the trinomial below?
3x³ - 24x² + 45x
a. 3x(x - 3)(x - 5)
b. 3x(x - 3)(x + 5)
c. 3(x - 3)(x + 5)
d. 3(x² - 3)(x + 5)

Explanation:

Step1: Factor out the GCF

The greatest common factor (GCF) of \(3x^{3}\), \(-24x^{2}\), and \(45x\) is \(3x\). Factoring out \(3x\) gives:
\(3x(x^{2}-8x + 15)\)

Step2: Factor the quadratic

We need to factor \(x^{2}-8x + 15\). We look for two numbers that multiply to \(15\) and add to \(-8\). The numbers are \(-3\) and \(-5\) because \((-3)\times(-5)=15\) and \((-3)+(-5)=-8\). So, \(x^{2}-8x + 15=(x - 3)(x - 5)\).

Step3: Combine the factors

Putting it all together, the factorization of \(3x^{3}-24x^{2}+45x\) is \(3x(x - 3)(x - 5)\).

Answer:

A. \(3x(x - 3)(x - 5)\)