Question

question 7 of 10
what is the factorization of the trinomial below?
$x^3 - 12x^2 + 35x$

a. $(x - 7)(x + 5)$
b. $(x^2 - 7)(x + 5)$
c. $x(x - 7)(x - 5)$
d. $x(x - 7)(x + 5)$

Explanation:

Step1: Factor out the GCF

The greatest common factor (GCF) of \(x^{3}\), \(- 12x^{2}\) and \(35x\) is \(x\). So we factor out \(x\) from the trinomial:
\(x^{3}-12x^{2}+35x=x(x^{2}-12x + 35)\)

Step2: Factor the quadratic

Now we need to factor the quadratic \(x^{2}-12x + 35\). We need two numbers that multiply to \(35\) and add up to \(- 12\). The numbers \(-7\) and \(-5\) satisfy this because \((-7)\times(-5)=35\) and \(-7+( - 5)=-12\). So we can factor \(x^{2}-12x + 35\) as \((x - 7)(x - 5)\).

Step3: Combine the factors

Putting it all together, the factorization of \(x^{3}-12x^{2}+35x\) is \(x(x - 7)(x - 5)\).

Answer:

C. \(x(x - 7)(x - 5)\)