How do you factor, ab + 3b + 2a + 6?

Question

Factroing, please help me solve and explain.

Answer 1

You factor by grouping.

 

(ab + 3b) + (2a +6)

 

Then you take out like terms, you need to make sure the terms left in the () are the same.

 

b(a + 3) + 2(a + 3)

 

This can now be written as:

 

(b + 2)(a + 3)

 

And you're done!

 

You can check it by FOILing it back into the polynomial:

 

ab + 3b + 2a +6

Answer 2

ab + 3b + 2a + 6

 

Now, you need a in one of your parentheses, and b in the other, so that when they are multiplied together their product will be ab:

(a + ___)(b + ___)

 

We know that our two numbers must multiply to have a product of 6. Also, since a and b each have their own constant associated with them, we've got to make sure our 3 gets multiplied by b and our 2 gets multiplied by a:

(a + 3)(b + 2)

 

That's it! Now if you want to check your answer, you can take your answer and multiply it out to see what you get.