how can I factor this problem a^2 +11ab +30b^2

Question

factoring polymonials

 helpme factor this problem

 

Answer 1

As I said in my comment, I suspect you typed this question incorrectly because as stated (a² + 11b + 30b) cannot be factored.  However, it can be easily factored if you typed all a's or all b's, and there shouldn't be a variable on the third value so I'm going to type an answer presumptively that this was the case.

 

When you multiply two binomials, you go through a process called FOIL: you multiple the first, outside, inside, and last values, then add them as appropriate.  Factoring a polynomial is simply the same process in reverse.

 

First, write the polynomial and two pairs of empty parentheses below it.

 

b² + 11b + 30

(       )(       )

 

First, let's factor the first value in the polynomial: b².  This is easy because there's only one way you can factor is out: b × b.  So we'll right those as the first values in our parentheses.

 

b² + 11b + 30
(b      )(b      )

 

Next, we need to add mathematical operators, which is just a fancy way to say plus or minus signs.  This depends on the third value in the polynomial, 30b.  Because 30b is a positive value, we'll use either two pluses or two minuses.  Because the second value is positive, we'll use two pluses.  If it was negative, we would use two minuses but this isn't the case.

 

b² + 11b + 30
(b +    )(b +   )

 

Next, we need to factor 30.  There are a number of ways to do this.  Possibilities include:

 

1 × 30

2 × 15

3 × 10

5 × 6

 

The trick is that we want to choose two factors that add up to the numerical portion of the second value in the polynomial, 11.  This means the correct factors to use are 5 and 6.  We put those in the last place of our two parentheses.

 

b² + 11b + 30
(b + 5)(b + 6)

 

There we have it, a factored polynomial: b² + 11b + 30 = (b + 5)(b + 6)

 

Just to make sure, let's check our work.  We'll take the factored polynomial (b + 5)(b + 6) and apply the FOIL technique to see if we get the original value of b2 + 11b + 30.  To do this, we'll multiply the First, Outside, Inside, and Last pairs of values.  This will yield for values that we'll then combine arithmetically.

 

First: b × b = b²

Outside: b × 6 = 6b

Inside: 5 × b = 5b

Last: 5 × 6 = 30

 

Combine those into a single mathematical expression and we get this:

 

b² + 6b + 5b + 30

 

And when we combine those values mathematically, we get this:

 

b² + 11b + 30

 

Indicating we factored the problem correctly.

Answer 2

How can I factor this problem

a^2 +11ab +30b^2?

=(a+5b)(a+6b)