polynomials factoring

Question

 

15x² + 26x+7

Answer 1

Lets do each part separately:

 

First off, all numbers in the expression are positive, which means all parts of the factored form will be positive as well.

 

The factored form is going to look like:

(nx + a)(mx + b)

 

The first term is 15x^2. The factors of 15 are

1 * 15

3 * 5

 

Therefore n = 1 and m = 15, OR n = 3 and m = 5

 

The last term is 7. The factors of 7 are:

1 * 7

 

Therefore a must = 1 and b must = 7

(nx + 1)(mx + 7)

 

The second term is 26x. 

We know that nx*7 + mx*1 = 26x, or 7n+m = 26

 

So now lets go through the possible values for n and m from the very beginning:

 

if n = 1, m = 15. Does this work? 7(1) + 15 = 22, which is not 26, so this doesn't work.

if n = 3, m = 5. Does this work? 7(3) + 5 = 21 + 5 = 26. This works.

 

Therefore, n = 3 and m = 5, and the factored form is:

(3x + 1)(5x + 7)

Answer 2

=(3x+1)(5x+7).

 

This is easy because 7 has only factors 1 and 7, so all you had to do was split 15 into two factors and choose an arrangement that produces +26x when you check it by the FOIL process.

Answer 3

You can also use the AC method.  I find this method to be more efficient in factoring trinomials of degree 2.

 

Multiply the coefficient of the first term and the last term together.

 

15 * 7 = 105

 

 

Now we find two numbers that multiply to 105, but add to 26.

 

5 and 21 are those numbers.

 

 

So now we have

 

15x² + 5x + 21x + 7

 

 

Factor by grouping.

 

5x(3x + 1) + 7(3x + 1)

 

 

The common factor here is (3x+1).

 

(3x + 1)(5x + 7)