# How do you factor a trinomial? ?

20a²b - 25ab + 45ab²

### 16 Answers

- 2 months ago
Factor out 5ab.

Divide each term by 5ab.

20a²b - 25ab + 45ab²

Answer: 5ab(4a - 5 + 9b)

You can also write the answer as

5ab(4a + 9b - 5)

Either one is acceptable.

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- AmyLv 72 months ago
Use the Distributive Property to remove any factor common to all terms.

14x²z + 28xyz + 35xz = 7xz(2x + 4y + 5)

That's all that can be done to the example you gave.

But if you end up with powers of variables in the form {x^2, xy, y^2}, it is sometimes possible to factor it further. This form includes {x^2, x, 1} and higher powers such as {x^6, x^3 y, y^2}

You can use the Quadratic Formula, use logic to guess at likely factors and check whether they divide the trinomial, or guess-and-check how to split the middle term in order to use the distributive property again.

4x^2 - 5x - 9 = 4x^2 + 4x - 9x - 9 = (x+1)(4x - 9)

- davidLv 72 months ago
There are different kinds of trinomials. You should be learning some patterns which will allow you to know which kind of trinomial this is and what kind of factoring to use. 1st 'rule' of factoring is to look for a greatest common factor. Look at the coefficients .. is there a common factor? 20, 25, and 45 are all multiples of 5 .. 5 is their GCF.

.. next look at the variables from each term

a^2b, ab, ab^2 <<<< each have both an a and b ... so the GCF for the variables is ab

20a^2b - 25ab + 45ab^2

= (5ab)(4a) - (5ab)(5) + (5ab)(9b)

= (5ab)(4a - 5 + 9b) >> answer

- Ian HLv 72 months ago
In this example just find the most that all 3 terms have in common.

20a^2b - 25ab + 45ab^2

They all have at least one a.

They all have at least one b.

The highest common factor of 20, 25 and 45 is just 5.

If you divide 20a^2b - 25ab + 45ab^2 by 5ab

you get 4a – 5 + 9b so you now know that

20a^2b - 25ab + 45ab^2 = 5ab(4a – 5 + 9b)