Question

factorise the following x^3+13x^2+32x+20

Answer 1

Answer:

Factors are (x + 2), (x + 10), (x + 1)

Step-by-step explanation:

f(x) = x³ + 13x² + 32x + 20

Using trial and error method, We assume x = 1, then

f(x) = 1³ + 13 (1²) + 32 (1) + 20

= 1 + 13 + 32 + 20 = 66 which is not equal to 0

If x = -1

f(x) = (-1³) + 13 (-1²) + 32 (-1) + 20

= -1 + 13 - 32 + 20 = 0

Therefore, x = -1 => (x + 1) is a factor of f(x)

(x³ + 13x² + 32x + 20) ÷ (x + 1) = x² + 12x + 20

By Splitting the middle term method, x² + 12x + 20 can be expressed as

x² + 10x + 2x + 20 [The product of the middle terms = 20x² ( x²×20) & Sum of the middle terms = 12x]

Taking the common factors out,we get

x(x + 10) + 2(x + 10)

=> (x + 2) (x + 10)

Therefore, Factors of f(x) are (x + 1) (x + 2) (x + 10)