what is the completely factored form of $3x^{5}-7x^{4}+6x^{2}-14x$?\n$(x^{4}+2x)(3x - 7)$\n$x^{4}(3x - 7)(2x…

what is the completely factored form of $3x^{5}-7x^{4}+6x^{2}-14x$?\n$(x^{4}+2x)(3x - 7)$\n$x^{4}(3x - 7)(2x - 1)$\n$x(x^{3}+2)(3x - 7)$\n$x(3x^{4}-7x^{3}+6x - 14)$

what is the completely factored form of $3x^{5}-7x^{4}+6x^{2}-14x$?\n$(x^{4}+2x)(3x - 7)$\n$x^{4}(3x - 7)(2x - 1)$\n$x(x^{3}+2)(3x - 7)$\n$x(3x^{4}-7x^{3}+6x - 14)$

Answer

Explanation:

Step1: Factor out the greatest - common factor

First, find the GCF of the terms $3x^{5}-7x^{4}+6x^{2}-14x$. The GCF of $3x^{5}, - 7x^{4},6x^{2},-14x$ is $x$. So, $3x^{5}-7x^{4}+6x^{2}-14x=x(3x^{4}-7x^{3}+6x - 14)$.

Step2: Group the terms

Group the terms inside the parentheses: $x((3x^{4}-7x^{3})+(6x - 14))$.

Step3: Factor out the common factors from each group

From the first group $3x^{4}-7x^{3}$, the common factor is $x^{3}$, so $3x^{4}-7x^{3}=x^{3}(3x - 7)$. From the second group $6x - 14$, the common factor is $2$, so $6x - 14 = 2(3x - 7)$.

Step4: Factor out the common binomial factor

We have $x(x^{3}(3x - 7)+2(3x - 7))$. Now, factor out the common binomial factor $(3x - 7)$: $x(3x - 7)(x^{3}+2)$.

Answer:

C. $x(x^{3}+2)(3x - 7)$