How To Factor Trinomials
In this article, we study about factoring How to Factor trinomials ?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 numbersbecause numbers are all like terms, which we can
add , subtract, etc. Also numbers we are familiar with tables and know the divisibility rulesfor 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.
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How to Factor Trinomials
Students can learn How to Factor Trinomials from the application of the formula
and solving problems on similar lines.
[delta] = [((-b/(2a)+-sqrt(b^2-4ac)/(2a))]
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.
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Factoring Trinomials Worksheets
Factorize:1. x2-3x-70
2. x2-18x+81
3. x2+2+ [1/x^2]
4. 2x2-8x-6
i . Find the constant a and b
1. x2-ax+b = (x-1)(x-8)
2. x2-2ax+a2 = (x-3)2
3. x2-ax-b = (x-7)(x+1)
i i. Word problems:
1.A number added to 7 and multiplied by the number added to 3 gives 21, Find the number
2. A number twice added to 7 multiplied by 3 less than the number gives 57. Find the number
3. The square of a number subtracted from 95 gives square of the difference of number and 1Find the number.
4. A number when added to two and multiplied by3 gives the square of the number +2. Find the number.
Answers:
i.(x-1)2,(x-9)2, (x+ [1/x] )2,2(x2-4x-3)
i . (-9,8),(a=3),(-6,-7)
i i.0, 3,7,4.
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