Factor completely: 5x3 + 15x2 + 10x

-5x • (x + 2) • (x + 1)

Step-by-step explanation:

Reformatting the input:

Changes made to your input should not affect the solution:

(1) : "x2" was replaced by "x^2". 1 more similar replacement (s).

Step by step solution:

Step 1:

Equation at the end of step 1:

((0 - (5 • (x3))) - (3•5x2)) - 10x

Step 2:

Equation at the end of step 2:

((0 - 5x3) - (3•5x2)) - 10x

Step 3:

Step 4:

Pulling out like terms:

4.1 Pull out like factors:

-5x3 - 15x2 - 10x = - 5x • (x2 + 3x + 2)

Trying to factor by splitting the middle term

4.2 Factoring x2 + 3x + 2

The first term is, x2 its coefficient is 1.

The middle term is, + 3x its coefficient is 3.

The last term, "the constant", is + 2

Step-1 : Multiply the coefficient of the first term by the constant 1 • 2 = 2

Step-2 : Find two factors of 2 whose sum equals the coefficient of the middle term, which is 3.

-2 + - 1 = - 3

-1 + - 2 = - 3

1 + 2 = 3 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 1 and 2

x2 + 1x + 2x + 2

Step-4 : Add up the first 2 terms, pulling out like factors:

x • (x+1)

Add up the last 2 terms, pulling out common factors:

2 • (x+1)

Step-5 : Add up the four terms of step 4:

(x+2) • (x+1)

Which is the desired factorization

Final result:

-5x • (x + 2) • (x + 1)