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How to Factor Trinomials

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In this article, we study about factoring trinomials. How to Factor Trinomials are defined in Mathematics an expression containing 3 unlike terms. For example, xz+y-2 is a trinomial, whereas x2-3X-X is not a trinomial as this can be simplified in to a binomial. So for an expression to be a trinomial, we have 3 terms which cannot be further simplified. The degree of the trinomial is the highest degree in the expression. If the highest degree of all variables put together is 2 then it is called quadratic and if it is 3, then it is cubic function. Factoring trinomials is complicated than factoring numbers because numbers are all like terms, which we can add , subtract, etc. Also numbers we are familiar with tables and know the divisibility rules for 2,3, 9, etc. But for expressions also we can become well-versed by continuous practice and doing exercises. Understanding the concept of factoring trinomials whenever it is of a square form, or whether +ve sign is there, or -ve sign is there, if we understand then factorization will be one step further. The advantage of How to Factor Trinomials is that its degree normally does not exceed 2. Hence quadratic formula we can apply if we cannot find exact splitting up of the x term. Eg: x2-2x-1 is of degree 2 whereas x4-x2-1 is a trinomial of degree 4. Factoring trinomials can be done in any of the following ways. We already know these identities as (a+b)2 = a2+2ab+b2 (a-b)2 = a2-2ab+b2 (x+a)(x+b) = x2+x(a+b)+ab These can be applied in reverse to factoring trinomials of this form. Example: Factorize x2-6x+9 This is of the form x2-2(x)(3)+32 . So factors are (x+3)2 Next is factorise 25x2-50x+1 = (5x)2-2(5x)(1)+1 = (5x-1)2 Thus these type of terms can be easily factored. Hence given a polynomial we check whether it is a quadratic with on variable, if it is so, check whether first term and last term is a square. If it is satisfied then check for
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How to Factor Trinomials
In this article, we study about factoring trinomials. How to Factor Trinomials are defined in Mathematics an
expression containing 3 unlike terms. For example, xz+y-2 is a trinomial, whereas x2-3X-X is not a trinomial
as this can be simplified in to a binomial. So for an expression to be a trinomial, we have 3 terms which
cannot be further simplified. The degree of the trinomial is the highest degree in the expression. If the highest
degree of all variables put together is 2 then it is called quadratic and if it is 3, then it is cubic function.
Factoring trinomials is complicated than factoring numbers because numbers are all like terms, which we can
add , subtract, etc. Also numbers we are familiar with tables and know the divisibility rules for 2,3, 9, etc. But
for expressions also we can become well-versed by continuous practice and doing exercises. Understanding
the concept of factoring trinomials whenever it is of a square form, or whether +ve sign is there, or -ve sign is
there, if we understand then factorization will be one step further. The advantage of
How to Factor Trinomials is that its degree normally does not exceed 2. Hence quadratic formula we can
apply if we cannot find exact splitting up of the x term.
Eg: x2-2x-1 is of degree 2 whereas x4-x2-1 is a trinomial of degree 4.
Factoring trinomials can be done in any of the following ways. We already know these identities as
(a+b)2 = a2+2ab+b2
(a-b)2 = a2-2ab+b2
(x+a)(x+b) = x2+x(a+b)+ab
These can be applied in reverse to factoring trinomials of this form.
Example: Factorize x2-6x+9
This is of the form x2-2(x)(3)+32 . So factors are (x+3)2
Next is factorise 25x2-50x+1 = (5x)2-2(5x)(1)+1 = (5x-1)2
T

hus these type of terms can be easily factored. H

ence given a polynomial we check whether it is a quadratic
with on variable, if it is so, check whether first term and last term is a square. If it is satisfied then check for

How to Factor How to Factor Trinomials can learn How to Factor Trinomials from the application of the
formula and solving problems on similar lines.1. Factoring trinomials Example : i. x2-3x-4: Here we have - sign
for ab. So for -4 we must have two factors such that their sum if -3. -4=-4*1, -4+1=-3.So we can factorise as (x-
4)(x+1).2. Factoring trinomials Example of x2+7x-30. In this problem, ab =-30, and their sum is +7. So suitable
factors are -10 *3 = -30. So answer is (x+10)(x-3).3. Factoring trinomials Example of the type: where a gcf is
there.
3x2-9x-3 = 3(x2-3x-1)
4. Factoring trinomials Examples of x2-2xy-3y2.
This is also similar to the factoring trinomials as (x+a)(x+b) only in that instead of a, b, y terms wil be there
5. How to Factor Trinomials when rational roots are not there.
Factoring trinomials like this also is possible upto 2 or 3 decimal places.
Eg: x2-x-3 . We want to factorise it. In this, 3 cannot be factored so that the sum is -1.
Hence we apply the formula. x=1/2a{-1
So x = 1+root 13/2 or 1- root 13/2
=2.3 or -1.3
So we get factors as (x-2.3)(x+1.3).
This is the approximate factorization upto 1 decimal<br>



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