3x^3 - 10x^2 + 70x

Question

Ho do you factor this trinomial?

Answer 1

The first step is to factor out any common factors.  

So, I see a single factor of x that is in common in all terms.  

So that makes it x(3x² -10x + 70).

 

Now to determine if the trinomial in parentheses is factorable you may try this method, called the British Method of Factoring:  Using the form ax² + bx + c, find [ac] (absolute value).  In this case it would be [3*70] = [210]=210.  Now list pairs of factors of 210 and the Sums and the Differences of each pair of factors:

1 * 210  209, 211

2 *105   107, 103

3 * 70    73,  67

5 * 42    47,  35

6 * 35    41,  29

7 * 30    37,  23

10 * 21  31,  11

14 * 15  29,  1

Look for a sum or difference that is b or -b, in your case 10 or -10.  If you find it then you use those factors; but in your case, we did not find a sum or difference that makes 10 or -10.  So your answer stays unchanged from factoring out the common factor.  

 

Here is a link to the British Method of Factoring Trinomials for your review:

 http://www.ohiorc.org/orc_documents/orc/richproblems/pm-draft-documents/pm-a18-bollenbacher-solution.pdf

Answer 2

3x³ - 10x² + 70x

 

let's factor out an x:

 

x(3x² - 10x + 70)

 

this is as far as we can go