Which polynomial has 5x + 2 as a factor?

Question

Which polynomial has 5x + 2 as a factor?

 

A.10x²-x-5

B.10x²-6x-10

C.15x²-9x-6

D.15x²+x+4

 

Answer 1

This problem requires you to look at each of the possible solutions and determine whether 5x+2 will work as one of the two factors of the second order polynomial. So they have given you one facotr, noe you have to determine if there is another factor that you can FOIL with (5x+2) to get the polynomial.

 

A. 10x²-x-5 = (5x+2)(ax+b)

 

This is how you should set up each and then try to determine if there is any positive or negative integers a and b that will work. In the case for choice A, there is not. You know that when you FOIL the two binomials, the last terms in each (2 and b) must multiply together to give the constant term in the polynomial. So you can see that there is no integer that will multiply by 2 to give 5.

 

Look at each answer choice this way and eventually you can find one where (5x+2) works as a factor.

 

C. 15x²-9x-6 can be factored into (5x+2)(3x-3)

 

You can see that if you FOIL this, you get

 

15x² - 15x + 6x - 6

 

which simplifies to

 

15x² - 9x - 6