Question

factor completely 3x^4 - 30x^3 + 75x^2.
3(x - 5)^2
3x^2(x - 5)^2
3x^2(x^2 - 10x + 25)
3x^2(x + 5)(x - 5)

Explanation:

Step1: Factor out GCF

First, find the greatest - common factor (GCF) of the terms $3x^{4}$, $-30x^{3}$, and $75x^{2}$. The GCF of 3, - 30, and 75 is 3, and the GCF of $x^{4}$, $x^{3}$, and $x^{2}$ is $x^{2}$. So, $3x^{4}-30x^{3}+75x^{2}=3x^{2}(x^{2}-10x + 25)$.

Step2: Factor the quadratic

The quadratic expression $x^{2}-10x + 25$ is a perfect - square trinomial of the form $a^{2}-2ab + b^{2}=(a - b)^{2}$, where $a = x$ and $b = 5$. So, $x^{2}-10x + 25=(x - 5)^{2}$.

Answer:

$3x^{2}(x - 5)^{2}$