How do you factor #10x^3 +15x^2 +20x#?

1 Answer
Oct 30, 2016

Answer:

# 10x^3 +15x^2 + 20x = 5x(2x^2+3x+4) #

Explanation:

We want to factorise # 10x^3 +15x^2 + 20x #

We can see immediately that #5x# is a common factor, so first lets factor that out:

# 10x^3 +15x^2 + 20x = 5x(2x^2+3x+4) #

We then check the discriminant of the quadratic factor, which is
# Delta = b^2-4ac = 9-4(2)(4) < 0 #
so we know the quadratic has no real roots, hence it has no real factors (By the factor theorem)

Hence, # 10x^3 +15x^2 + 20x = 5x(2x^2+3x+4) #