205k views
4 votes
What is the quotient (6x^4+15x^3+10x^2+10x+4)/(3x^2+2)

User Triamus
by
8.0k points

1 Answer

5 votes

Answer:

(2x + 1) • (x + 2)

Explanation:

Step 1 :

Equation at the end of step 1 :

(((15 • (x3)) - (2•5x2)) + 6x) - 4

Step 2 :

Equation at the end of step 2 :

(((3•5x3) - (2•5x2)) + 6x) - 4

Step 3 :

Checking for a perfect cube :

3.1 15x3-10x2+6x-4 is not a perfect cube

Trying to factor by pulling out :

3.2 Factoring: 15x3-10x2+6x-4

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: 6x-4

Group 2: 15x3-10x2

Pull out from each group separately :

Group 1: (3x-2) • (2)

Group 2: (3x-2) • (5x2)

-------------------

Add up the two groups :

(3x-2) • (5x2+2)

Which is the desired factorization

User Rkoval
by
7.2k points