Question

Factor the polynomial f(x) = X^3+5x^2+7X+3

Answer 1

The answer is (X+1)^2(x+3)

Answer 2

Explanation:

Third level polynomial, so three factors

Only whole numbers, so only whole number x⁰ factors

whole number factors of 3 are 1,1,3 or 1,-1,-3 or -1,-1,3

let's try (x + 3) as a factor

x² + 2x + 1

x + 3 | x³ + 5x² + 7x + 3

- x³ + 3x²

2x² + 7x

- 2x² + 6x

x + 3

- x + 3

0

so (x + 3) is a factor and x² + 2x + 1 factors to (x + 1)²

x³ + 5x² + 7x + 3 = (x + 3)(x + 1)(x + 1)