How do you factor x^5+5x^4+6x^3?

2 Answers
Nov 5, 2016

x^5+5x^4+6x^3 = x^3(x+2)(x+3)

Explanation:

First note that all of the terms are divisible by x^3, so we can separate that out as a factor first:

x^5+5x^4+6x^3 = x^3(x^2+5x+6)

To factor the remaining quadratic, we want to find two numbers whose sum is 5 and whose product is 6, since in general we have:

(x+p)(x+q) = x^2+(p+q)x+pqx

The numbers 2, 3 work, so we have:

x^2+5x+6 = (x+2)(x+3)

Putting it all together:

x^5+5x^4+6x^3 = x^3(x+2)(x+3)

Nov 5, 2016

x^3(x+3)(x+2)

Explanation:

Factorization is accomplished by taking a common factor ,completing the square, applying the polynomial identities ,or using the quadratic formula .

x^5+5x^4+6x^3
=color(blue)(x^3)color(brown)((x^2+5x+6)

The expression x^2+5x+6 can be factorized using the trial and error method, in other words, the idea is to find two integers whose sum is color(red) 5 and their product is color(violet) 6.

X^2+color(red)SX+color(violet)P

For the expression x^2+5x+6 , the two integers satisfying the color(red)S and color(violet)P requirements are 3 and 2.

color(brown)(x^2+5x+6=(x+3)(x+2))

For the whole expression\ x^5+5x^4+6x^3\ , the factorized form is:

color(blue)(x^3)color(brown)((x+3)(x+2)

Therefore,

x^5+5x^4+6x^3=x^3(x+3)(x+2)