Question

What is the factorization of the trinomial below? x3 - 12x2 + 35x

Answer 1

Answer:

x(x - 5)(x - 7)

Step-by-step explanation:

Given

x³ - 12x² + 35x ← factor out common factor of x from each term

= x(x² - 12x + 35)

To factor the quadratic

Consider the factors of the constant term (+ 35) which sum to give the coefficient of the x- term (- 12)

The factors are - 5 and - 7, since

- 5 × - 7 = 35 and - 5 - 7 = - 12, thus

x² - 12x + 35 = (x - 5)(x - 7) and

x³ - 12x² + 35x = x(x - 5)(x - 7) ← in factored form