Define trinomial or what is a trinomial?
A trinomial is a polynomial which consists of three monomials. For example: - 3x^2 + 4x - 8, 6m^2 + 4m+9 and 5x^3 + 3x^2 + 6x etc. all are the examples of trinomials.
Factoring trinomials
A trinomial exactly has three terms. Two trinomials always have same number of terms but their degree may differ. For example we may have two degree trinomial or three degree polynomial. A trinomial can be factored into its factors which when multiplied gives the same trinomial. A trinomial which is in a quadratic form that is with degree two can be factored using the quadratic formula. A polynomial with a degree greater than 2 can be first simplified by taking the common factors. If the trinomial is in a quadratic form such as ax^2 + bx +c, for factorization we follow the following steps:-
• Identify the values of a, b and c in the trinomial ax^2+ bx + c.
• Write down all the factors of ‘a*c’.
• Identify which factor pair sums to the value of ‘b’.
Adding and Subtracting trinomials
Adding trinomials
Trinomials can be added by simply adding the like terms together. For example: - The term with the same variables are added together. For example: - Add (3x^2 + 4x + 5) to (6x^3 + 9x^2 + 5)
= 3x^2 + 4x + 5 + 6x^3 + 9x^2 + 5
= 6x^3 + 12x^2 + 4x + 10
Subtracting trinomials
The terms of the trinomials can only be added or subtracted if the variables are same. The first step is to remove the brackets and put the like terms together that is the terms with same variables together and then perform the operations. For example: - (4x^2 + 7x - 2) – (2x^2 + 8x - 9)
= 4x^2 + 7x – 2 – 2x^2 - 8x + 9
= 4x^2 – 2x^2 + 7x – 8x – 2 + 9
= 2x^2 – x + 7
This is the resultant trinomial.
A trinomial, ax^2 + bx + c is called a perfect square trinomial if b^2 = 4ac
A perfect square trinomial is obtained when we multiply a binomial by itself; the resulting polynomial is known as Perfect square trinomial. For example : - (x-2) is a binomial. If we multiply (x-2) by itself we will get (x-2) (x-2) which is equal to x^2 + 4 - 4x which is a perfect square trinomial.
A trinomial is a polynomial which consists of three monomials. For example: - 3x^2 + 4x - 8, 6m^2 + 4m+9 and 5x^3 + 3x^2 + 6x etc. all are the examples of trinomials.
Factoring trinomials
A trinomial exactly has three terms. Two trinomials always have same number of terms but their degree may differ. For example we may have two degree trinomial or three degree polynomial. A trinomial can be factored into its factors which when multiplied gives the same trinomial. A trinomial which is in a quadratic form that is with degree two can be factored using the quadratic formula. A polynomial with a degree greater than 2 can be first simplified by taking the common factors. If the trinomial is in a quadratic form such as ax^2 + bx +c, for factorization we follow the following steps:-
• Identify the values of a, b and c in the trinomial ax^2+ bx + c.
• Write down all the factors of ‘a*c’.
• Identify which factor pair sums to the value of ‘b’.
Adding and Subtracting trinomials
Adding trinomials
Trinomials can be added by simply adding the like terms together. For example: - The term with the same variables are added together. For example: - Add (3x^2 + 4x + 5) to (6x^3 + 9x^2 + 5)
= 3x^2 + 4x + 5 + 6x^3 + 9x^2 + 5
= 6x^3 + 12x^2 + 4x + 10
Subtracting trinomials
The terms of the trinomials can only be added or subtracted if the variables are same. The first step is to remove the brackets and put the like terms together that is the terms with same variables together and then perform the operations. For example: - (4x^2 + 7x - 2) – (2x^2 + 8x - 9)
= 4x^2 + 7x – 2 – 2x^2 - 8x + 9
= 4x^2 – 2x^2 + 7x – 8x – 2 + 9
= 2x^2 – x + 7
This is the resultant trinomial.
A trinomial, ax^2 + bx + c is called a perfect square trinomial if b^2 = 4ac
A perfect square trinomial is obtained when we multiply a binomial by itself; the resulting polynomial is known as Perfect square trinomial. For example : - (x-2) is a binomial. If we multiply (x-2) by itself we will get (x-2) (x-2) which is equal to x^2 + 4 - 4x which is a perfect square trinomial.
