Question

What is the multi-step factor of: x^4-14x^3+13x^2

Answer 1

x²(x - 1)(x - 13)

Explanation:

`x^(4)` - 14x³ + 13x² ← factor out x² from each term

= x²(x² - 14x + 13) ← factor the quadratic

consider the factors of the constant term (+ 13) which sum to give the coefficient of the x- term (- 14)

the factors are - 1 and - 13 , since

- 1 × - 13 + = 13 and - 1 - 13 = - 14 , then

x² - 14x + 13 = (x - 1)(x - 13)

and

`x^(4)` - 14x³ + 13x² = x²(x - 1)(x - 13)